Gated voltammetry

ABSTRACT

A sensor system, device, and methods for determining the concentration of an analyte in a sample is described. Gated voltammetric pulse sequences including multiple duty cycles of sequential excitations and relaxations may provide a shorter analysis time and/or improve the accuracy and/or precision of the analysis. The disclosed pulse sequences may reduce analysis errors arising from the hematocrit effect, variance in cap-gap volumes, non-steady-state conditions, mediator background, a single set of calibration constants, under-fill, and changes in the active ionizing agent content of the sensor strip.

REFERENCE TO RELATED APPLICATIONS

This application is a continuation of PCT/US2006/035129 entitled “GatedVoltammetry” filed Sep. 11, 2006, which was published in English andclaimed the benefit of U.S. Provisional Application No. 60/722,584entitled “Gated Voltammetry” as filed on Sep. 30, 2005, each of whichare incorporated herein by reference.

BACKGROUND

The quantitative determination of analytes in biological fluids isuseful in the diagnosis and treatment of physiological abnormalities.For example, determining the glucose level in biological fluids, such asblood, is important to diabetic individuals who must frequently checktheir blood glucose level to regulate their diets and/or medication.

Electrochemical systems have been used for this type of analysis. Duringthe analysis, the analyte undergoes a redox reaction with an enzyme orsimilar species to generate an electric current that may be measured andcorrelated with the concentration of the analyte. A substantial benefitmay be provided to the user by decreasing the time required for theanalysis while supplying the desired accuracy and precision.

One example of an electrochemical sensor system for analyzing analytesin biological fluids includes a measuring device and a sensor strip. Thesensor strip includes reagents to react with and transfer electrons fromthe analyte during the analysis and electrodes to pass the electronsthrough conductors to the device. The measuring device includes contactsto receive the electrons from the strip and the ability to apply avoltage differential between the contacts. The device may record thecurrent passing through the sensor and translate the current values intoa measure of the analyte content of the sample. These sensor systems mayanalyze a single drop of whole blood (WB), such as from 1-15 microliters(μL) in volume.

Examples of bench-top measuring devices include the BAS100B Analyzeravailable from BAS Instruments in West Lafayette, Ind.; the CHInstrument Analyzer available from CH Instruments in Austin, Tex.; theCypress Electrochemical Workstation available from Cypress Systems inLawrence, Kans.; and the EG&G Electrochemical Instrument available fromPrinceton Research Instruments in Princeton, N.J. Examples of portablemeasuring devices include the Ascensia Breeze® and Elite® meters ofBayer Corporation.

The sensor strip may include a working electrode where the analyteundergoes electrochemical reaction and a counter electrode where theopposite electrochemical reaction occurs, thus allowing current to flowbetween the electrodes. Thus, if oxidation occurs at the workingelectrode, reduction occurs at the counter electrode. See, for example,Fundamentals Of Analytical Chemistry, 4^(th) Edition, D. A. Skoog and D.M. West; Philadelphia: Saunders College Publishing (1982), pp 304-341.

The sensor strip also may include a true reference electrode to providea non-variant reference potential to the measuring device. Whilemultiple reference electrode materials are known, a mixture of silver(Ag) and silver chloride (AgCl) is typical due to the insolubility ofthe mixture in the aqueous environment of the analysis solution. Areference electrode also may be used as the counter electrode. A sensorstrip using such a combination reference-counter electrode is describedin U.S. Pat. No. 5,820,551.

The sensor strip may be formed by printing electrodes on an insulatingsubstrate using multiple techniques, such as those described in U.S.Pat. Nos. 6,531,040; 5,798,031; and 5,120,420. One or more reagent layermay be formed by coating one or more of the electrodes, such as theworking and/or counter electrodes. In one aspect, more than one of theelectrodes may be coated by the same reagent layer, such as when theworking and counter electrodes are coated by the same composition. Inanother aspect, reagent layers having different compositions may beprinted or micro-deposited onto the working and counter electrodes usingthe method described in a U.S. provisional patent application filed Oct.24, 2003, Ser. No. 60/513,817. Thus, the reagent layer on the workingelectrode may contain the enzyme, the mediator, and a binder while thereagent layer on the counter electrode contains a soluble redox species,which could be the same as the mediator or different, and a binder.

The reagent layer may include an ionizing agent for facilitating theoxidation or reduction of the analyte, as well as any mediators or othersubstances that assist in transferring electrons between the analyte andthe conductor. The ionizing agent may be an analyte specific enzyme,such as glucose oxidase or glucose dehydrogenase, to catalyze theoxidation of glucose in a WB sample. The reagent layer also may includea binder that holds the enzyme and mediator together. Table I, below,provides conventional combinations of enzymes and mediators for use withspecific analytes.

TABLE I Analyte Enzyme Mediator Glucose Glucose Oxidase FerricyanideGlucose Glucose Dehydrogenase Ferricyanide Cholesterol CholesterolOxidase Ferricyanide Lactate Lactate Oxidase Ferricyanide Uric AcidUricase Ferricyanide Alcohol Alcohol Oxidase Phenylenediamine

The binder may include various types and molecular weights of polymers,such as CMC (carboxylmethyl cellulose) and/or PEO (polyethylene oxide).In addition to binding the reagents together, the binder may assist infiltering red blood cells, preventing them from coating the electrodesurface.

Examples of conventional electrochemical sensor systems for analyzinganalytes in biological fluids include the Precision® biosensorsavailable from Abbott in Abbott Park, Ill.; Accucheck® biosensorsavailable from Roche in Indianapolis, Ind.; and OneTouch Ultra®biosensors available from Lifescan in Milpitas, Calif.

One electrochemical method, which has been used to quantify analytes inbiological fluids, is coulometry. For example, Heller et al. describedthe coulometric method for WB glucose measurements in U.S. Pat. No.6,120,676. In coulometry, the analyte concentration is quantified byexhaustively oxidizing the analyte within a small volume and integratingthe current over the time of oxidation to produce the electrical chargerepresenting the analyte concentration. Thus, coulometry captures thetotal amount of analyte present within the sensor strip.

An important aspect of coulometry is that towards the end of theintegration curve of charge vs. time, the rate at which the currentchanges with time becomes substantially constant to yield a steady-statecondition. This steady-state portion of the coulometric curve forms arelatively flat plateau region, thus allowing determination of thecorresponding current. However, the coulometric method requires thecomplete conversion of the entire volume of analyte to reach thesteady-state condition. As a result, this method is time consuming anddoes not provide the fast results which users of electrochemicaldevices, such as glucose-monitoring products, demand. Another problemwith coulometry is that the small volume of the sensor cell must becontrolled in order to provide accurate results, which can be difficultwith a mass produced device.

Another electrochemical method which has been used to quantify analytesin biological fluids is amperometry. In amperometry, current is measuredduring a read pulse as a constant potential (voltage) is applied acrossthe working and counter electrodes of the sensor strip. The measuredcurrent is used to quantify the analyte in the sample. Amperometrymeasures the rate at which the electrochemically active species, such asthe analyte, is being oxidized or reduced near the working electrode.Many variations of the amperometric method for biosensors have beendescribed, for example in U.S. Pat. Nos. 5,620,579; 5,653,863;6,153,069; and 6,413,411.

A disadvantage of conventional amperometric methods is thenon-steady-state nature of the current after a potential is applied. Therate of current change with respect to time is very fast initially andbecomes slower as the analysis proceeds due to the changing nature ofthe underlying diffusion process. Until the consumption rate of thereduced mediator at the electrode surface equals the diffusion rate, asteady-state current cannot be obtained. Thus, for conventionalamperometry methods, measuring the current during the transient periodbefore a steady-state condition is reached may be associated with moreinaccuracy than a measurement taken during a steady-state time period.

The “hematocrit effect” provides an impediment to accurately analyzingthe concentration of glucose in WB samples. WB samples contain red blood(RB) cells and plasma. The plasma is mostly water, but contains someproteins and glucose. Hematocrit is the volume of the RB cellconstituent in relation to the total volume of the WB sample and isoften expressed as a percentage. Whole blood samples generally havehematocrit percentages ranging from 20% to 60%, with ˜40% being theaverage.

In conventional sensor strips, glucose may be oxidized by an enzyme,which then transfers the electron to a mediator. This reduced mediatorthen travels to the working electrode where it is electrochemicallyoxidized. The amount of mediator being oxidized may be correlated to thecurrent flowing between the working and counter electrodes of the sensorstrip. Quantitatively, the current measured at the working electrode isdirectly proportional to the diffusion coefficient of the mediator. Thehematocrit effect interferes with this process because the RB cellsblock the diffusion of the mediator to the working electrode.Subsequently, the hematocrit effect influences the amount of currentmeasured at the working electrode without any connection to the amountof glucose in the sample.

WB samples having varying concentrations of RB cells may causeinaccuracies in the measurement because the sensor may not distinguishbetween a lower mediator concentration and a higher mediatorconcentration where the RB cells block diffusion to the workingelectrode. For example, when WB samples containing identical glucoselevels, but having hematocrits of 20, 40, and 60%, are analyzed, threedifferent glucose readings will be reported by a conventional sensorsystem based on one set of calibration constants (slope and intercept,for instance). Even though the glucose concentrations are the same, thesystem will report that the 20% hematocrit sample contains more glucosethan the 60% hematocrit sample due to the RB cells interfering withdiffusion of the mediator to the working electrode.

The normal hematocrit range (RBC concentration) for humans is from 20%to 60% and is centered around 40%. Hematocrit bias refers to thedifference between the reference glucose concentration obtained with areference instrument, such as the YSI 2300 STAT PLUST™ available fromYSI Inc., Yellow Springs, Ohio, and an experimental glucose readingobtained from a portable sensor system for samples containing differinghematocrit levels. The difference between the reference and experimentalreadings results from the varying hematocrit levels between specific WBsamples.

In addition to the hematocrit effect, measurement inaccuracies also mayarise when the measurable species concentration does not correlate withthe analyte concentration. For example, when a sensor system determinesthe concentration of a reduced mediator generated in response to theoxidation of an analyte, any reduced mediator not generated by oxidationof the analyte will lead to the sensor system indicating that moreanalyte is present in the sample than is correct due to mediatorbackground.

In addition to the hematocrit and mediator background effects, otherfactors also may lead to inaccuracies in the ability of a conventionalelectrochemical sensor system to determine the concentration of ananalyte in a sample. In one aspect, these inaccuracies may be introducedbecause the portion of the sensor strip that contains the sample mayvary in volume from strip to strip. Inaccuracies also may be introducedwhen sufficient sample is not provided to completely fill the volume ofthe cap-gap, a condition referred to as under-fill. In other aspects,inaccuracies may be introduced into the measurement by random “noise”and when the sensor system lacks the ability to accurately determinetemperature changes in the sample.

In an attempt to overcome one or more of these disadvantages,conventional sensor systems have attempted multiple techniques, not onlywith regard to the mechanical design of the sensor strip and reagentselection, but also regarding the manner in which the measuring deviceapplies the electric potential to the strip. For example, conventionalmethods of reducing the hematocrit effect for amperometric sensorsinclude the use of filters, as disclosed in U.S. Pat. Nos. 5,708,247 and5,951,836; reversing the polarity of the applied current, as disclosedin WO 01/57510; and by methods that maximize the inherent resistance ofthe sample, as disclosed in U.S. Pat. No. 5,628,890.

Multiple methods of applying the electric potential to the strip,commonly referred to as pulse methods, sequences, or cycles, have beenused to address inaccuracies in the determined analyte concentration.For example, in U.S. Pat. No. 4,897,162 the pulse method includes acontinuous application of rising and falling voltage potentials that arecommingled to give a triangular-shaped wave. Furthermore, WO 2004/053476and U.S. Pat. Documents 2003/0178322 and 2003/0113933 describe pulsemethods that include the continuous application of rising and fallingvoltage potentials that also change polarity.

Other conventional methods combine a specific electrode configurationwith a pulse sequence adapted to that configuration. For example, U.S.Pat. No. 5,942,102 combines the specific electrode configurationprovided by a thin layer cell with a continuous pulse so that thereaction products from the counter electrode arrive at the workingelectrode. This combination is used to drive the reaction until thecurrent change verses time becomes constant, thus reaching a true steadystate condition for the mediator moving between the working and counterelectrodes during the potential step. While each of these methodsbalances various advantages and disadvantages, none are ideal.

As may be seen from the above description, there is an ongoing need forimproved electrochemical sensor systems, especially those that mayprovide increasingly accurate determination of the analyte concentrationin less time. The systems, devices, and methods of the present inventionovercome at least one of the disadvantages associated with conventionalsystems.

SUMMARY

A voltammetric method of determining the concentration of an analyte ina sample is provided that includes applying a pulse sequence to thesample and measuring the resulting currents, the pulse sequence includesat least two duty cycles. In addition to the at least two duty cycles,the pulse sequence may include a terminal read pulse and/or an initialtime delay and may be applied to a sensor strip including a diffusionbarrier layer on a working electrode. The method may include less biasattributable to mediator background than a concentration of the analytedetermined from another method or from a voltammetric method lacking thepulse sequence comprising at least two duty cycles. The sample may be aliquid including a biological fluid and the analyte may be glucose.

The duty cycles may include an excitation including a potential variedwith time or a potential varied linearly with time, such as a linear,cyclic, acyclic, or a combination of these excitation types. A currentvalue may be recorded during each of the excitations and the pulsesequence may include a terminal read pulse. The duty cycles may includeacyclic excitations substantially excluding a reverse oxidation peak ora reverse reduction peak and may reduce the concentration of a mediatorin the sample not responsive to the analyte in relation to the methodwhere the duty cycles comprise cyclic excitations. The duty cycles mayinclude acyclic excitations terminating before initiation of a reversecurrent peak, acyclic excitations substantially excluding forward andreverse oxidation and reduction peaks, or acyclic excitationssubstantially within a diffusion limited current region of a redox pair.

The method may include the determination of at least one contour profileand may include applying at least one data treatment, such assemi-integral, semi-derivative, or derivative, to the resultingcurrents. The method also may include determining a plurality ofcalibration sets from the currents and determining the number of dutycycles from the plurality of calibration sets. Determination of theanalyte concentration may include averaging multiple concentrationvalues obtained from the plurality of calibration sets.

The method also may include determining if a sensor strip containing thesample is under-filled with the sample. This determination may includecomparing at least one current value to a pre-selected value. The methodalso may include determining the active ionizing agent content of asensor strip, a determination that may be made by determining a ratiofrom forward and reverse scan current values. In one aspect, this ratiowas previously correlated to known amounts of the active ionizing agent.In another aspect, a calibration slope may be altered in response to theactive ionizing agent content of the sensor strip. In another aspect,the excitation/relaxation time ratio of the duty cycles may be from 0.3to 0.2.

A handheld analyte measuring device is provided for determining theconcentration of an analyte in a sample. The device includes a gatedvoltammetric measuring device adapted to receive a sensor strip. Thegated amperometric measuring device includes at least two devicecontacts in electrical communication with a display through electricalcircuitry. The sensor strip includes at least first and second sensorstrip contacts. The first sensor strip contact is in electricalcommunication with a working electrode and the second sensor stripcontact is in electrical communication with a counter electrode throughconductors. A first reagent layer is on at least one of the electrodesand includes an oxidoreductase and at least one species of a redox pair.The electrodes may be on the same or on different substrates.

A handheld measuring device adapted to receive a sensor strip isprovided for determining the concentration of an analyte in a sample.The device includes contacts, at least one display, and electroniccircuitry establishing electrical communication between the contacts andthe display. The circuitry includes an electric charger and a processor,where the processor is in electrical communication with a computerreadable storage medium. The medium includes computer readable softwarecode, which when executed by the processor, causes the charger toimplement a gated voltammetric pulse sequence including at least twoduty cycles.

A method of reducing the bias attributable to mediator background in adetermined concentration of an analyte in a sample is provided thatincludes applying a gated voltammetric pulse sequence including at leasttwo duty cycles.

A method of determining the duration of a pulse sequence including atleast 2 duty cycles, for determining the concentration of an analyte ina sample is provided that includes determining a plurality of sets ofcalibration constants determined from currents recorded during the atleast 2 duty cycles and determining the duration of the pulse sequencein response to the determined concentration of the analyte in thesample. The pulse sequence may be a gated voltammetric pulse sequence.

A method of signaling a user to add additional sample to a sensor stripis provided that includes determining if the sensor strip isunder-filled by comparing at least one current value recorded from apulse sequence including at least 2 duty cycles to a pre-selected valueand signaling the user to add additional sample to the sensor strip ifthe strip is under-filled. The pulse sequence may be a gatedvoltammetric pulse sequence. The sensor strip may include two electrodesand the determining may be performed in less than five seconds.

A voltammetric method of determining the concentration of an analyte ina sample is provided that includes applying a pulse sequence to thesample and measuring the resulting currents, the pulse sequence includesat least 2 duty cycles having excitation/relaxation time ratios from 0.3to 0.2. The method may be more accurate than a concentration of theanalyte determined from another method where the excitation/relaxationtime ratio of a pulse is greater than 0.3.

An electrochemical method for determining the concentration of ananalyte in a sample is provided that includes an improvement includingapplying a gated voltammetric pulse sequence to the sample including atleast two duty cycles.

The following definitions are included to provide a clear and consistentunderstanding of the specification and claims.

The term “analyte” is defined as one or more substances present in asample. The analysis determines the presence and/or concentration of theanalyte present in the sample.

The term “sample” is defined as a composition that may contain anunknown amount of the analyte. Typically, a sample for electrochemicalanalysis is in liquid form, and preferably the sample is an aqueousmixture. A sample may be a biological sample, such as blood, urine, orsaliva. A sample also may be a derivative of a biological sample, suchas an extract, a dilution, a filtrate, or a reconstituted precipitate.

The term “voltammetry” is defined as an analysis method where theconcentration of an analyte in a sample is determined byelectrochemically measuring the oxidation or reduction rate of theanalyte at a varying potential.

The term “system” or “sensor system” is defined as a sensor strip inelectrical communication through its conductors with a measuring device,which allows for the quantification of an analyte in a sample.

The term “sensor strip” is defined as a device that contains the sampleduring the analysis and provides electrical communication between thesample and the measuring device. The portion of the sensor strip thatcontains the sample is often referred to as the “cap-gap.”

The term “conductor” is defined as an electrically conductive substancethat remains stationary during an electrochemical analysis.

The term “measuring device” is defined as one or more electronic devicesthat may apply an electric potential to the conductors of a sensor stripand measure the resulting current. The measuring device also may includethe processing capability to determine the presence and/or concentrationof one or more analytes in response to the recorded current values.

The term “accuracy” is defined as how close the amount of analytemeasured by a sensor strip corresponds to the true amount of analyte inthe sample. In one aspect, accuracy may be expressed in terms of bias.

The term “precision” is defined as how close multiple analytemeasurements are for the same sample. In one aspect, precision may beexpressed in terms of the spread or variance among multiplemeasurements.

The term “redox reaction” is defined as a chemical reaction between twospecies involving the transfer of at least one electron from a firstspecies to a second species. Thus, a redox reaction includes anoxidation and a reduction. The oxidation half-cell of the reactioninvolves the loss of at least one electron by the first species, whilethe reduction half-cell involves the addition of at least one electronto the second species. The ionic charge of a species that is oxidized ismade more positive by an amount equal to the number of electronsremoved. Likewise, the ionic charge of a species that is reduced is madeless positive by an amount equal to the number of electrons gained.

The term “mediator” is defined as a substance that may be oxidized orreduced and that may transfer one or more electrons. A mediator is areagent in an electrochemical analysis and is not the analyte ofinterest, but provides for the indirect measurement of the analyte. In asimplistic system, the mediator undergoes a redox reaction in responseto the oxidation or reduction of the analyte. The oxidized or reducedmediator then undergoes the opposite reaction at the working electrodeof the sensor strip and is regenerated to its original oxidation number.

The term “binder” is defined as a material that provides physicalsupport and containment to the reagents while having chemicalcompatibility with the reagents.

The term “mediator background” is defined as the bias introduced intothe measured analyte concentration attributable to measurable speciesnot responsive to the underlying analyte concentration.

The term “measurable species” is defined as any electrochemically activespecies that may be oxidized or reduced under an appropriate potentialat the working electrode of an electrochemical sensor strip. Examples ofmeasurable species include analytes, oxidoreductases, and mediators.

The term “under-fill” is defined as when insufficient sample wasintroduced into the sensor strip to obtain an accurate analysis.

The term “redox pair” is defined as two conjugate species of a chemicalsubstance having different oxidation numbers. Reduction of the specieshaving the higher oxidation number produces the species having the loweroxidation number. Alternatively, oxidation of the species having thelower oxidation number produces the species having the higher oxidationnumber.

The term “oxidation number” is defined as the formal ionic charge of achemical species, such as an atom. A higher oxidation number, such as(III), is more positive, and a lower oxidation number, such as (II), isless positive.

The term “reversible redox pair” is defined as a pair of redox specieswhere the separation between the forward and reverse scans of thesemi-integral is at most 30 mV at the half-height of the si_(ss)transition. For example, in FIG. 10A the forward and reversesemi-integral scans for the ferricyanide/ferrocyanide redox pair inaddition to the si_(ss) transition height are shown. At the line wherethe half-height si_(ss) transition line intersects the forward andreverse scan lines the separation between the lines is 29 mV,establishing the reversibility of the ferricyanide/ferrocyanide redoxpair at the depicted scan rate.

The term “quasi-reversible redox pair” is defined as a redox pair wherethe separation between the forward and reverse scans of thesemi-integral is larger than 30 mV at the half-height of the si_(ss)transition for the redox pair.

The term “soluble redox species” is defined as a substance that iscapable of undergoing oxidation or reduction and that is soluble inwater (pH 7, 25° C.) at a level of at least 1.0 grams per Liter. Solubleredox species include electro-active organic molecules, organotransitionmetal complexes, and transition metal coordination complexes. The term“soluble redox species” excludes elemental metals and lone metal ions,especially those that are insoluble or sparingly soluble in water.

The term “oxidoreductase” is defined as any enzyme that facilitates theoxidation or reduction of an analyte. An oxidoreductase is a reagent.The term oxidoreductase includes “oxidases,” which facilitate oxidationreactions where molecular oxygen is the electron acceptor; “reductases,”which facilitate reduction reactions where the analyte is reduced andmolecular oxygen is not the analyte; and “dehydrogenases,” whichfacilitate oxidation reactions where molecular oxygen is not theelectron acceptor. See, for example, Oxford Dictionary of Biochemistryand Molecular Biology, Revised Edition, A. D. Smith, Ed., New York:Oxford University Press (1997) pp. 161, 476, 477, and 560.

The term “electro-active organic molecule” is defined as an organicmolecule lacking a metal that is capable of undergoing an oxidation orreduction reaction. Electro-active organic molecules may serve asmediators.

The term “organotransition metal complex,” also referred to as “OTMcomplex,” is defined as a complex where a transition metal is bonded toat least one carbon atom through a sigma bond (formal charge of −1 onthe carbon atom sigma bonded to the transition metal) or a pi bond(formal charge of 0 on the carbon atoms pi bonded to the transitionmetal). For example, ferrocene is an OTM complex with twocyclopentadienyl (Cp) rings, each bonded through its five carbon atomsto an iron center by two pi bonds and one sigma bond. Another example ofan OTM complex is ferricyanide (III) and its reduced ferrocyanide (II)counterpart, where six cyano ligands (formal charge of −1 on each of the6 ligands) are sigma bonded to an iron center through the carbon atoms.

The term “coordination complex” is defined as a complex havingwell-defined coordination geometry, such as octahedral or square planar.Unlike OTM complexes, which are defined by their bonding, coordinationcomplexes are defined by their geometry. Thus, coordination complexesmay be OTM complexes (such as the previously mentioned ferricyanide), orcomplexes where non-metal atoms other than carbon, such as heteroatomsincluding nitrogen, sulfur, oxygen, and phosphorous, are datively bondedto the transition metal center. For example, ruthenium hexaamine is acoordination complex having a well-defined octahedral geometry where sixNH₃ ligands (formal charge of 0 on each of the 6 ligands) are dativelybonded to the ruthenium center. A more complete discussion oforganotransition metal complexes, coordination complexes, and transitionmetal bonding may be found in Collman et al., Principles andApplications of Organotransition Metal Chemistry (1987) and Miessler &Tarr, Inorganic Chemistry (1991).

The term “steady-state” is defined as when the change in electrochemicalsignal (current) with respect to its independent input variable (voltageor time) is substantially constant, such as within ±10 or ±5%.

The term “relatively constant” is defined as when the change in acurrent value or a diffusion rate is within ±20, ±10, or ±5%.

The term “reversing-point” is defined as the point in a cyclic oracyclic scan when the forward scan is stopped and the reverse scan isinitiated.

The term “linear excitation” is defined as an excitation where thevoltage is varied in a single “forward” direction at a fixed rate, suchas from −0.5 V to +0.5 V to provide a 1.0 V excitation range. Theexcitation range may cover the reduced and oxidized states of a redoxpair so that a transition from one state to the other occurs. A linearexcitation may be approximated by a series of incremental changes inpotential. If the increments occur very close together in time, theycorrespond to a continuous linear excitation. Thus, applying a change ofpotential approximating a linear change may be considered a linearexcitation.

The term “cyclic excitation” is defined as a combination of a linearforward excitation and a linear reverse excitation where the excitationrange includes the oxidation and reduction peaks of a redox pair. Forexample, varying the potential in a cyclic manner from −0.5 V to +0.5 Vand back to −0.5 V is an example of a cyclic excitation for theferricyanide/ferrocyanide redox pair as used in a glucose sensor, whereboth the oxidation and reduction peaks are included in the excitationrange.

The term “acyclic excitation” is defined in one aspect as an excitationincluding more of one forward or reverse current peak than the othercurrent peak. For example, an excitation including forward and reverselinear excitations where the forward excitation is started at adifferent voltage than where the reverse excitation stops, such as from−0.5 V to +0.5 V and back to +0.25 V, is an example of an acyclicexcitation. In another example, an acyclic excitation may start and endat substantially the same voltage when the excitation is started at most±20, ±10, or ±5 mV away from the formal potential E^(o)′ of the redoxpair. In another aspect, an acyclic excitation is defined as anexcitation including forward and reverse linear excitations thatsubstantially exclude the oxidation and reduction peaks of a redox pair.For example, the excitation may begin, reverse, and end within thediffusion-limited region of a redox pair, thus excluding the oxidationand reduction peaks of the pair.

The terms “fast excitation,” “fast excitation rate,” “fast scan,” and“fast scan rate” are defined as an excitation where the voltage ischanged at a rate of at least 176 mV/sec. Preferable fast excitationrates are rates greater than 200, 500, 1,000, or 2,000 mV/sec.

The terms “slow excitation,” “slow excitation rate,” “slow scan,” and“slow scan rate” are defined as an excitation where the voltage ischanged at a rate of at most 175 mV/sec. Preferable slow excitationrates are rates slower than 150, 100, 50, or 10 mV/sec.

The term “average initial thickness” refers to the average height of alayer prior to the introduction of a liquid sample. The term average isused because the top surface of the layer is uneven, having peaks andvalleys.

The term “redox intensity” (RI) is defined as the total excitation timedivided by the sum of the total excitation time and the total relaxationtime delays for a pulse sequence.

The term “handheld device” is defined as a device that may be held in ahuman hand and is portable. An example of a handheld device is themeasuring device accompanying Ascensia® Elite Blood Glucose MonitoringSystem, available from Bayer HealthCare, LLC, Elkhart, Ind.

The term “on” is defined as “above” and is relative to the orientationbeing described. For example, if a first element is deposited over atleast a portion of a second element, the first element is said to be“deposited on” the second. In another example, if a first element ispresent above at least a portion of a second element, the first elementis said to be “on” the second. The use of the term “on” does not excludethe presence of substances between the upper and lower elements beingdescribed. For example, a first element may have a coating over its topsurface, yet a second element over at least a portion of the firstelement and its top coating may be described as “on” the first element.Thus, the use of the term “on” may or may not mean that the two elementsbeing related are in physical contact.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention may be better understood with reference to the followingdrawings and description. The components in the figures are notnecessarily to scale, emphasis instead being placed upon illustratingthe principles of the invention. Moreover, in the figures, likereferenced numerals designate corresponding parts throughout thedifferent views.

FIG. 1A is a perspective representation of an assembled sensor strip.

FIG. 1B is a top-view diagram of a sensor strip, with the lid removed.

FIG. 2 depicts an end-view diagram of the sensor strip of FIG. 1B.

FIGS. 3A and 3B depict a working electrode having a surface conductorand a DBL during the application of long and short read pulses.

FIGS. 4A and 4B are graphs illustrating the improvement in measurementaccuracy when a DBL is combined with a short excitation.

FIG. 5 represents an electrochemical analytic method of determining thepresence and concentration of an analyte in a sample.

FIGS. 6A-6F represent six examples of pulse sequences where multipleduty cycles were applied to the sensor strip after introduction of thesample.

FIG. 7A is a graph showing a cyclic voltammogram from a sensor system.

FIG. 7B compares a cyclic scan to an acyclic scan, where the forwardexcitation of the acyclic scan was started near the formal potentialE^(o)′ for the redox pair.

FIG. 7C shows an acyclic scan, where the reverse scan is terminated thereverse current peak.

FIG. 7D shows a cyclic scan with an acyclic scan superimposed in the DLCregion.

FIGS. 8A-8D shows the output currents plotted as voltammograms from thepulse sequence represented in FIG. 6C for 40% hematocrit WB samplescontaining 50, 100, and 400 mg/dL glucose

FIGS. 9A-9C show contour profiles of the voltammograms of FIGS. 8A-8C.

FIG. 10A is a graph of the semi-integral corresponding to the cyclicvoltammogram of FIG. 7A.

FIG. 10B presents the semi-integral of the acyclic data corresponding tothe acyclic voltammogram of FIG. 7C.

FIG. 10C presents the semi-integrals of the cyclic and acyclicexcitations of FIG. 7B.

FIG. 10D shows the semi-integral and recorded current values for theacyclic excitation of FIG. 7D.

FIG. 11 shows contour profiles prepared by semi-integratingvoltammograms from a seven excitation pulse sequence for WB samplescontaining varying amounts of glucose.

FIG. 12A depicts the cyclic voltammogram, semi-integral, andsemi-derivative of 16 mM ferrocyanide in a 20% hematocrit WB sample.

FIG. 12B is an enlargement of the semi-derivative curve of FIG. 12A.

FIGS. 13A-13C depict the derivatives of cyclic voltammograms.

FIG. 14 plots the semi-integral currents recorded as a function of timefor the contour profiles of FIG. 11.

FIG. 15 depicts the cyclic voltammograms obtained from an under-filledsensor strip.

FIG. 16A depicts semi-integral plots of cyclic voltammograms obtainedfrom five sensor strips with 1 V/sec scan rates for a sample including100 mg/dL glucose and 400% hematocrit in WB.

FIG. 16B plots the ratio of the forward and reverse scan current valuestaken at the 0.15 potential as a function of enzyme concentration.

FIG. 16C depicts a typical response of the slope of the linear responsecalibration of the sensor strip as a function of the GO content (%-dryweight).

FIG. 17 is a schematic representation of a measuring device.

DETAILED DESCRIPTION

An electrochemical analytic system determines the concentration ofanalytes in a sample, such as the glucose concentration of whole blood.The system includes at least one device that applies gated voltammetricpulse sequences including multiple duty cycles to the sample. Each dutycycle includes a linear, cyclic, or acyclic excitation during whichcurrents (amperage) are measured from a sensor strip while a potential(voltage) applied to the strip is varied linearly with time. Each dutycycle also includes a relaxation that may be provided by an opencircuit. The system may compare the resulting current data to determinethe concentration of the analyte in the sample, while correcting theresults for variations in non-analyte responsive factors. The systemalso may apply one or more data treatments, including those based onsemi-integration, derivatives, and semi-derivatives to analyze thevoltammetric data.

The gated voltammetric pulse sequences may provide improved accuracy andprecision to the analysis, while reducing the completion time of theanalysis. Accuracy errors introduced by the hematocrit effect andprecision errors introduced by varying cap-gap volume may be reducedthrough the combination of a diffusion barrier layer with the gatedpulse sequences. Errors otherwise resulting from a non-steady-statesensor condition and/or mediator background also may be reduced. Thetime required for analysis may be reduced by eliminating the need foradditional delays and pulses, such as “incubation” delays to providereagent rehydration, “burn-off” pulses to renew the electrodes, andmediator regeneration pulses to renew the oxidation state of themediator. The gated pulse sequences also may allow the determination ofdynamic current and contour profiles that provide multiple calibrationpoints, under-fill detection, and the ability to apply temperaturecompensation to the analysis. Because the gated pulse sequences maygenerate useful data rapidly, the long wait times of conventionalcoulometry and the inaccuracy of non-steady-state measurements inconventional amperometry may be avoided.

FIGS. 1A-1B depict a sensor strip 100, which may be used in the presentsensor system. FIG. 1A is a perspective representation of an assembledsensor strip 100 including a sensor base 110, at least partially coveredby a lid 120 that includes a vent 130, a concave area 140, and an inputend opening 150. A partially-enclosed volume 160 (the cap-gap) is formedbetween the base 110 and the lid 120. Other sensor strip designscompatible with the present invention also may be used, such as thosedescribed in U.S. Pat. Nos. 5,120,420 and 5,798,031.

A liquid sample for analysis may be transferred into the cap-gap 160 byintroducing the liquid to the opening 150. The liquid fills the cap-gap160 while expelling the previously contained air through the vent 130.The cap-gap 160 may contain a composition (not shown) that assists inretaining the liquid sample in the cap-gap. Examples of suchcompositions include water-swellable polymers, such as carboxymethylcellulose and polyethylene glycol; and porous polymer matrices, such asdextran and polyacrylamide.

FIG. 1B depicts a top-view of the sensor strip 100, with the lid 120removed. Conductors 170 and 180 may run under a dielectric layer 190from the opening 150 to a working electrode 175 and a counter electrode185, respectively. In one aspect, the working and counter electrodes175, 185 may be in substantially the same plane, as depicted in thefigure. In another aspect, the electrodes 175, 185 may be facing, suchas described in U.S. Pat. App. 2004/0054267.

While the working and counter electrodes 175, 185 may be closer, in oneaspect the electrodes 175, 185 may be separated by greater than 200 or250 μm. Similarly, while at least one of the electrodes 175, 185 may becloser, in one aspect at least one electrode may be separated from anupper portion of the lid 120 by at least 100 μm. In one aspect, theworking and counter electrodes 175, 185 may have surface areas ofapproximately 1 mm² and 1.2 mm², respectively. The dielectric layer 190may partially cover the electrodes 175, 185 and may be made from anysuitable dielectric material, such as an insulating polymer.

The counter electrode 185 balances the potential at the workingelectrode 175 of the sensor strip 100. In one aspect, this potential maybe a reference potential achieved by forming the counter electrode 185from a redox pair, such as Ag/AgCl, to provide a combinedreference-counter electrode. In another aspect, the potential may beprovided to the sensor system by forming the counter electrode 185 froman inert material, such as carbon, and including a soluble redoxspecies, such as ferricyanide, within the cap-gap 160.

Alternatively, the sensor strip 100 may be provided with a thirdconductor and electrode (not shown) to provide a reference potential tothe sensor system. This third electrode may be configured as a truereference electrode or as an inert material that relies on a solubleredox species to provide the reference potential. The third electrodealso may allow the measuring device to determine the insertion of asensor strip and/or if the cap-gap 160 has filled with sample.Additional conductors and/or electrodes also may be provided on thestrip 100 to provide these and other functions.

FIG. 2 depicts an end-view diagram of the sensor strip depicted in FIG.1B showing the layer structure of the working electrode 175 and thecounter electrode 185. The conductors 170 and 180 may lie directly onthe base 110. Surface conductor layers 270 and 280 optionally may bedeposited on the conductors 170 and 180, respectively. The surfaceconductor layers 270, 280 may be made from the same or from differentmaterials.

The material or materials used to form the conductors 170, 180 and thesurface conductor layers 270, 280 may include any electrical conductor.Preferable electrical conductors are non-ionizing, such that thematerial does not undergo a net oxidation or a net reduction duringanalysis of the sample. The conductors 170, 180 preferably include athin layer of a metal paste or metal, such as gold, silver, platinum,palladium, copper, or tungsten. The surface conductor layers 270, 280preferably include carbon, gold, platinum, palladium, or combinationsthereof. If a surface conductor layer is not present on a conductor, theconductor is preferably made from a non-ionizing material.

The surface conductor material may be deposited on the conductors 170,180 by any conventional means compatible with the operation of thesensor strip, including foil deposition, chemical vapor deposition,slurry deposition, metallization, and the like. In the case of slurrydeposition, the mixture may be applied as an ink to the conductors 170,180, as described in U.S. Pat. No. 5,798,031.

The reagent layers 275 and 285 may be deposited on the conductors 170and 180, respectively, and include reagents and optionally a binder. Thebinder material is preferably a polymeric material that is at leastpartially water-soluble. Suitable partially water-soluble polymericmaterials for use as the binder may include poly(ethylene oxide) (PEO),carboxy methyl cellulose (CMC), polyvinyl alcohol (PVA), hydroxyethylenecellulose (HEC), hydroxypropyl cellulose (HPC), methyl cellulose, ethylcellulose, ethyl hydroxyethyl cellulose, carboxymethyl ethyl cellulose,polyvinyl pyrrolidone (PVP), polyamino acids such as polylysine,polystyrene sulfonate, gelatin, acrylic acid, methacrylic acid, starch,maleic anhydride, salts thereof, derivatives thereof, and combinationsthereof. Among the above binder materials, PEO, PVA, CMC, and PVA arepreferred, with CMC and PEO being more preferred at present.

In addition to the binder, the reagent layers 275 and 285 may includethe same or different reagents. In one aspect, the reagents present inthe first layer 275 may be selected for use with the working electrode175, while the reagents present in the second layer 285 may be selectedfor use with the counter electrode 185. For example, the reagents in thelayer 285 may facilitate the free flow of electrons between the sampleand the conductor 180. Similarly, the reagents in the layer 275 mayfacilitate the reaction of the analyte.

The reagent layer 275 may include an oxidoreductase specific to theanalyte that may facilitate the reaction of the analyte while enhancingthe specificity of the sensor system to the analyte, especially incomplex biological samples. Examples of some specific oxidoreductasesand corresponding analytes are given below in Table II.

TABLE II Oxidoreductase (reagent layer) Analyte Glucose dehydrogenaseβ-glucose Glucose oxidase β-glucose Cholesterol esterase; cholesteroloxidase Cholesterol Lipoprotein lipase; glycerol kinase; glycerol-3-Triglycerides phosphate oxidase Lactate oxidase; lactate dehydrogenase;Lactate diaphorase Pyruvate oxidase Pyruvate Alcohol oxidase AlcoholBilirubin oxidase Bilirubin Uricase Uric acid Glutathione reductaseNAD(P)H Carbon monoxide oxidoreductase Carbon monoxideAt present, especially preferred oxidoreductases for glucose analysisinclude glucose oxidase, glucose dehydrogenase, derivatives thereof, orcombinations thereof.

The reagent layer 275 also may include a mediator to more effectivelycommunicate the results of the analyte reaction to the surface conductor270 and/or the conductor 170. Examples of mediators include OTMcomplexes, coordination complexes, and electro-active organic molecules.Specific examples include ferrocene compounds, ferrocyanide,ferricyanide, coenzymes of substituted or unsubstituted pyrroloquinolinequinones (PQQ), substituted or unsubstituted3-phenylimino-3H-phenothiazines (PIPT), 3-phenylimino-3H-phenoxazine(PIPO), substituted or unsubstituted benzoquinones, substituted orunsubstituted naphthoquinones, N oxides, nitroso compounds,hydroxylamines, oxines, flavins, phenazines, phenazine derivatives,phenothiazines, indophenols, and indamines. These, and other mediatorsthat may be included in the reagent layer may be found in U.S. Pat. Nos.5,653,863; 5,520,786; 4,746,607; 3,791,988; and in EP Pat. Nos. 0 354441 and 0 330 517.

At present, especially preferred mediators for glucose analysis includeferricyanide, ruthenium hexaamine, PIPT, PIPO, or combinations thereof.A review of useful electrochemical mediators for biological redoxsystems may be found in Analytica Clinica Acta. 140 (1982), pages 1-18.

The reagent layers 275, 285 may be deposited by any convenient means,such as printing, liquid deposition, or ink-jet deposition. In oneaspect, the layers are deposited by printing. With other factors beingequal, the angle of the printing blade may inversely affect thethickness of the reagent layers. For example, when the blade is moved atan approximately 82° angle to the base 110, the layer may have athickness of approximately 10 μm. Similarly, when a blade angle ofapproximately 62° to the base 110 is used, a thicker 30 μm layer may beproduced. Thus, lower blade angles may provide thicker reagent layers.In addition to blade angle, other factors, such as the viscosity of thematerial being applied as well as the screen-size and emulsioncombination, may affect the resulting thickness of the reagent layers275, 285.

The working electrode 175 also may include a diffusion barrier layer(DBL) that is integral to a reagent layer 275 or that is a distinctlayer 290, such as depicted in FIG. 2. Thus, the DBL may be formed as acombination reagent/DBL on the conductor, as a distinct layer on theconductor, or as a distinct layer on the reagent layer. When the workingelectrode 175 includes the distinct DBL 290, the reagent layer 275 mayor may not reside on the DBL 290. Instead of residing on the DBL 290,the reagent layer 275 may reside on any portion of the sensor strip 100that allows the reagent to solubilize in the sample. For example, thereagent layer 175 may reside on the base 110 or on the lid 120.

The DBL provides a porous space having an internal volume where ameasurable species may reside. The pores of the DBL may be selected sothat the measurable species may diffuse into the DBL, while physicallylarger sample constituents, such as RB cells, are substantiallyexcluded. Although conventional sensor strips have used variousmaterials to filter RB cells from the surface of the working electrode,a DBL provides an internal volume to contain and isolate a portion ofthe measurable species from the sample.

When the reagent layer 275 includes a water-soluble binder, any portionof the binder that does not solubilize into the sample prior to theapplication of an excitation may function as an integral DBL. Theaverage initial thickness of a combination DBL/reagent layer ispreferably less than 30 or 23 micrometers (μm) and more preferably lessthan 16 μm. At present, an especially preferred average initialthickness of a combination DBL/reagent layer is from 1 to 30 μm or from3 to 12 μm. The desired average initial thickness of a combinationDBL/reagent layer may be selected for a specific excitation length onthe basis of when the diffusion rate of the measurable species from theDBL to a conductor surface, such as the surface of the conductor 170 orthe surface of the surface conductor 270 from FIG. 2, becomes relativelyconstant.

Furthermore, using too thick of a DBL with a short excitation length maydelay when the diffusion rate of the measurable species from the DBL tothe conductor surface becomes relatively constant. For example, whenduty cycles including sequential 1 second excitations separated by 0.5second relaxations are applied to a working electrode using acombination DBL/reagent layer having an average initial thickness of 30μm, a preferred measurable species diffusion rate from the DBL to theconductor surface may not be reached until at least 6 duty cycles havebeen applied (>˜10 seconds). Conversely, when the same duty cycles areapplied to a working electrode using a combination DBL/reagent layerhaving an average initial thickness of 11 μm, a relatively constantdiffusion rate may be reached after the second excitation (˜2.5seconds). Thus, there is an upper limit for the preferred averageinitial thickness of the DBL for a given duty cycle. A more in-depthtreatment of the correlation between DBL thickness, excitation length,and time to reach a relatively constant diffusion rate may be found inWO 2006/042304, filed Oct. 12, 2005, entitled “ConcentrationDetermination in a Diffusion Barrier Layer”.

The distinct DBL 290 may include any material that provides the desiredpore space, while being partially or slowly soluble in the sample. Inone aspect, the distinct DBL 290 may include a reagent binder materiallacking reagents. The distinct DBL 290 may have an average initialthickness of at least 1 μm, preferably, from 5 to 25 μm, and morepreferably from 8 to 15 μm.

FIGS. 3A and 3B depict a working electrode 300 having a surfaceconductor 330 and a distinct DBL 305 during the application of long andshort read pulses. When a WB sample is applied to the working electrode300, RB cells 320 cover the DBL 305. Analyte present in the sample formsexternal measurable species 310 external to the DBL 305. A portion ofthe external measurable species 310 diffuses into the distinct DBL 305to give internal measurable species 315.

As shown in FIG. 3A, when a continuous 10 second read pulse is appliedto the working electrode 300, both the external and internal measurablespecies 310 and 315 are excited at the surface conductor 330 by a changein oxidation state. During the long read pulse, the external measurablespecies 310 diffuses through the sample region where the RB cells 320reside and through the DBL 305 to the surface conductor 330. Diffusionof the external measurable species 310 through the RB cells 320 duringthe read pulse introduces the hematocrit effect to the analysis. Becausea substantial portion of the measurable species excited at the surfaceconductor 330 originates from outside the DBL 320, a long read pulseapplied to a sensor strip having a DBL may perform similarly withregards to the hematocrit effect to a short read pulse applied to astrip lacking a DBL.

Conversely, FIG. 3B represents the situation where a short excitation isapplied to the DBL equipped sensor strip 300 to excite the internalmeasurable species 315, while substantially excluding from excitationthe measurable species 310 external to the DBL 305. During the shortexcitation, the measurable species 310 either remains external to theDBL 305 or does not substantially diffuse through the DBL to reach thesurface conductor 330. In this manner, the short excitation may providea substantial reduction in the influence of the hematocrit effect on theanalysis. By reducing the hematocrit effect, analysis errors (bias)introduced by the sample constituents, including RB cells, may bereduced.

Another advantage of selectively analyzing the measurable speciesinternal to the DBL with a short excitation is a reduction ofmeasurement imprecision from sensor strips having varying cap-gapvolumes. Variances in the cap-gap volume between sensor strips may leadto imprecision because the electronics in conventional measuring devicesapply the same electric potential and perform the same calculations foreach analysis. If a read pulse continues past the time whensubstantially all of the measurable species present in the cap-gap hasbeen analyzed, the analysis no longer represents the concentration ofmeasurable species in the sample, but instead represents the amount ofmeasurable species in the cap-gap; a very different measurement. Thus, asensor strip having a larger cap-gap volume will show a higher analyteconcentration than a sensor strip having a smaller cap-gap volume,independent of the analyte concentration of the sample. By substantiallylimiting analysis to the measurable species present in the DBL, theimprecision otherwise introduced by manufacturing variability betweensensor strips may be reduced.

FIGS. 4A and 4B are graphs illustrating the improvement in measurementaccuracy when a DBL was combined with a short excitation. FIG. 4A showsa large inaccuracy represented as the difference between the 16% and 48%calibration lines (the total hematocrit bias span) resulting from asensor strip lacking a DBL after a 1 second excitation. Conversely, FIG.4B shows a smaller difference between the calibration lines representinga more accurate result when a DBL was combined with a 1 secondexcitation. The total bias hematocrit span for the DBL combined with ashort excitation was nearly two-thirds less than the total bias spanwithout the DBL.

As described above and in further detail in WO 2006/042304, a short readpulse or excitation may provide an improvement in the accuracy and/orprecision of an analysis. However, if a single short excitation is usedfor the analysis, a relatively constant diffusion rate of the measurablespecies from the DBL to the conductor surface may not be reached duringthe analysis. This condition also may result in measurement inaccuracybecause the concentration of the measurable species within the DBL doesnot accurately represent that in the sample. Furthermore, the singleexcitation may not effectively reduce the background signal from themediator.

FIG. 5 represents an electrochemical analysis 500 for determining thepresence and optionally the concentration of an analyte 522 in a sample512 that may overcome the disadvantages associated with shortexcitations. In one aspect, the analysis 500 may reduce bias frommediator background while providing a shorter analysis time with orwithout a DBL. In a preferred aspect, the analysis 500 may be completedin less than 3 or less than 1 minute. In a more preferred aspect, theanalysis 500 may be completed in from 2 to 50 or from 4 to 32 seconds.

In 510, the sample 512 is introduced to a sensor strip 514, such as thesensor strip depicted in FIGS. 1A-1B and 2. The reagent layers, such as275 and/or 285 from FIG. 2, begin to solubilize into the sample 512,thus allowing reaction. At this point in the analysis, an initial timedelay, or “incubation period,” optionally may be provided for thereagents to react with the sample 512. Preferably, the optional timedelay may be from 1 to 10 seconds. A more in-depth treatment of initialtime delays may be found in U.S. Pat. Nos. 5,620,579 and 5,653,863. Inone aspect, the analysis 500 may reduce the need for an incubationperiod.

During the reaction, a portion of the analyte 522 present in the sample512 is chemically or biochemically oxidized or reduced in 520, such asby an oxidoreductase. Upon oxidation or reduction, electrons optionallymay be transferred between the analyte 522 and a mediator 532 in 530.

In 540, a measurable species 542, which may be the charged analyte 522from 520 or the charged mediator 532 from 530, is electrochemicallyexcited (oxidized or reduced). For example, when the sample 512 is wholeblood containing glucose oxidized by glucose oxidase in 520 andtransferring an electron to reduce a ferricyanide (III) mediator toferrocyanide (II) in 530, the excitation of 540 oxidizes ferrocyanide(II) to ferricyanide (III) at the working electrode. In this manner, anelectron is selectively transferred from the glucose analyte to theworking electrode of the sensor strip where it may be detected by ameasuring device (not shown).

The excitation 540 includes voltammetric scanning where a varyingpotential or “scan” is applied across the electrodes of the sensor strip514 at a substantially fixed rate (V/sec). The scan rate may be slow orfast; however, fast scans are preferred due to the nature of the gatedpulse sequences. In one aspect, the rate at which the potential isscanned is at least 2 mV/sec, preferably from 20 to 5000 mV/sec, morepreferably from 200 to 2000 mV/sec. At present, an especially preferredscan rate is from 500 to 1500 mV/sec.

The duration of the excitation 540 is at most 4 or 5 seconds, andpreferably less than 3, 2, 1.5, or 1 second. In another aspect, theduration of the excitation 540 is from 0.1 to 3 seconds, from 0.1 to 2seconds, or from 0.1 to 1.5 seconds. More preferably, the duration ofthe excitation 540 is from 0.4 to 1.2 seconds.

In 550, the currents resulting from the scanning excitation 540 may bemonitored and recorded as a function of the applied potential (voltage).This contrasts with conventional amperometry and coulometry where aconstant voltage is applied while the current is measured as a functionof time. In one aspect, the current is monitored and recorded during theexcitation 540. In another aspect, the current is not monitored duringthe relaxation 560 or at least during a portion of the relaxation 560.In another aspect, the current and the potential at the workingelectrode may be monitored during at least a portion of the relaxation560, but the values are not used in determining the concentration of theanalyte 522.

In 560, the sample undergoes relaxation, where the measuring device mayopen the circuit through the sensor strip 514, thus allowing the systemto relax. During the relaxation 560, the current applied during theexcitation 540 is substantially reduced by at least one-half, preferablyby an order of magnitude, and more preferably to zero. Preferably, azero current state is provided by an open circuit. In one aspect, therelaxation 560 is at least 10, 5, 3, 2, 1.5, 1, or 0.5 seconds induration. In another aspect, the relaxation 560 is from 0.1 to 3seconds, from 0.1 to 2 seconds, or from 0.1 to 1.5 seconds in duration.More preferably, the relaxation 360 is from 0.2 to 1.5 seconds induration and provided by an open circuit.

During the relaxation 560, the ionizing agent may react with the analyteto generate additional measurable species without the effects of anelectric potential. Thus, for a glucose sensor system including glucoseoxidase and a ferricyanide mediator as reagents, additional ferrocyanide(reduced mediator) responsive to the analyte concentration of the samplemay be produced without interference from an electric potential duringthe relaxation 560.

The excitation 540, the recordation 550, and the relaxation 560constitute a single duty cycle. In 570, the duty cycle is repeated atleast once for a total of at least two duty cycles. In one aspect, theduty cycle is repeated at least twice for a total of at least three dutycycles within 180 seconds, 90 seconds, or less.

In another aspect, the pulse sequence of the analysis 500 includes atleast 4, 6, 8, 10, 14, 18, or 22 duty cycles applied during anindependently selected 120, 90, 60, 30, 15, 10, or 5 second time period.In another aspect, the duty cycles are applied during a 5 to 60 secondtime period. In another aspect, from 3 to 18 or from 3 to 10 duty cyclesmay be applied within 30 seconds or less. In another aspect, from 4 to 8duty cycles may be applied within 3 to 16 seconds.

The repetitive “on” and “off” nature of the duty cycles of the analysis500 directly contrast with conventional methods where voltage iscontinuously applied to and current is continuously drawn from a sensorstrip for from 5 to 10 seconds during the duration of the read pulse.For these conventional methods, the applied voltage may have a fixedpotential or may have a potential that is swept from a positive to anegative potential or from a positive or a negative potential to a zeropotential relative to a reference potential. Even at a zero relativepotential, these methods continuously draw current from the sensor stripduring the read pulse, which permits the electrochemical reaction tocontinue throughout the read pulse. Thus, in these conventional methodsthe reaction that produces measurable species responsive to the analyteconcentration and the diffusion of the measurable species to the workingelectrode are both affected by current during the zero potential portionof a conventional read pulse. The analysis 500 pulse sequences also aremarkedly different from conventional methods that use a single longduration pulse with multiple measurements, such as those disclosed inU.S. Pat. No. 5,243,516, due to the multiple relaxations 560.

In 580, the recorded current and voltage values may be transformed withone or more data treatments. The transformed values may be used todetermine the presence and/or concentration of the analyte 522 in thesample 512. The transformed values also may be used to determine othercharacteristics of the analysis 500, including the hematocritconcentration of the sample, multiple calibration sets, under-fill, andthe active ionizing agent content of the sensor strip, as outlinedbelow.

FIGS. 6A-6F depict six examples of gated voltammetric pulse sequencesthat may be used with the method 500. In each pulse sequence, multipleduty cycles were applied to the sensor strip after introduction of thesample. The voltammetric excitation portion of each duty cycle may beapplied in a linear (FIG. 6A), cyclic (FIG. 6B), or acyclic manner(FIGS. 6C-6F). In these examples, tilted (linear) or triangular-wave(cyclic or acyclic) excitation pulses were used; however, other wavetypes compatible with the sensor system and the sample also may be used.

FIG. 6A depicts multiple tilted excitations where the voltage increasedlinearly with time to an endpoint. FIG. 6B depicts multipletriangular-wave excitations providing cyclic data that includes thecomplete potential range of the ferricyanide mediator. FIG. 6C depictssix duty cycles including six triangular-wave excitations providingacyclic data that starts and ends at substantially the same voltage.Because the last excitation of FIG. 6C, a terminal read pulse 640, lacksa relaxation, only six duty cycles are shown. FIG. 6D depicts seven dutycycles including seven triangular-wave excitations providing acyclicdata. The first duty cycle is preceded by an initial incubation period.FIG. 6E depicts multiple triangular-wave excitations providing acyclicdata that starts and ends at different voltages. FIG. 6F depictsmultiple triangular-wave excitations resulting in acyclic data thatsubstantially exclude the oxidation and reduction peaks of theferricyanide/ferrocyanide redox pair.

The terminal read pulse 640 may have the same duration and scan rate asthe excitations of the prior duty cycles, as depicted in FIG. 6C, or theterminal read pulse 640 may have a different duration or rate. In oneaspect, the terminal read pulse 640 may be of longer duration andincreased voltage in relation to the excitations of the prior dutycycles. The increased voltage may provide the ability to detect aspecies having a higher oxidation potential, such as a control solution.A more complete discussion regarding terminal read pulses may be foundin U.S. Provisional App. No. 60/669,729, filed Apr. 8, 2005, entitled“Oxidizable Species as an Internal Reference in Control Solutions forBiosensors.”

Control solutions containing known amounts of glucose may be used toverify that the analysis system is operating properly. Specificformulations for control solutions may be found in U.S. Pat. Nos.3,920,580; 4,572,899; 4,729,959; 5,028,542; 5,605,837; and PCTpublications WO 93/21928; WO 95/13535; and WO 95/13536. If themeasurement device cannot distinguish between a signal from a controlsolution versus a sample, control solution readings may be stored asanalyte values. Thus, the history of a patent's glucose readings, forexample, may be inaccurate regarding diabetic condition.

If the control solutions cannot be identified and their responsesseparated from those of the blood samples by the test meter, glucosereadings of the control solutions will be included in the history of theglucose measurements, which could lead to wrong interpretation of apatient's diabetic condition.

Each of the duty cycles for the pulse sequences depicted in FIGS. 6A-6Fprovide excitation times of shorter duration than the following opencircuit relaxation times; however, this is not required. In FIG. 6C theduration of the excitations is 0.8 seconds at a rate of 1 V/sec whilethe duration of each relaxation is about 3.2 seconds. Thus, each dutycycle has a duration of about 4 seconds and the pulse sequence lasts forabout 24.8 seconds, including a terminal read pulse to provide a redoxintensity (RI) of 0.226 (5.6/24.8). The pulse sequence of FIG. 6Dprovides a lower RI of 0.2 (5.6/28), attributable to the incubationperiod before the first duty cycle.

The higher the RI for a pulse sequence, the less background inaccuracyintroduced into the analysis by the mediator. The pulse sequencesrepresented in FIGS. 6A-6F are oxidative pulses, designed to excite(e.g. oxidize) a reduced mediator, which is the measurable species.Thus, the greater the oxidative current applied to the sensor strip in agiven time period, the less chance that mediator reduced by pathwaysother than oxidation of the analyte contributes to the recorded currentvalues. In combination, the multiple excitations of the gatedvoltammetric pulse sequence may eliminate the need for an initial pulseto renew the oxidation state of the mediator. For ferricyanide, pulsesequences having RI values of at least 0.01, 0.3, 0.6, or 1 arepreferred, with RI values of from 0.1 to 0.8, from 0.2 to 0.7, or from0.4 to 0.6 being more preferred at present.

During a linear excitation, such as forward excitation 610 depicted inFIG. 6A, the current at the working electrode is measured while thepotential at the working electrode changes linearly with time at aconstant rate. The excitation range, such as from −0.5 V to +0.5 V, maycover the reduced and oxidized states of a redox pair so that atransition from a first state to a second state occurs. The currentmeasured at the working electrode may be thought of as having threecomponents: the equilibrium current, the diffusion current, and thesurface current. The surface current, which may derive from any speciesadsorbed on the electrode, is generally small. The equilibrium anddiffusion currents are the primary components represented in theresulting voltammogram.

A linear voltammogram (a plot of current verses voltage) may becharacterized by a plot that starts at an initial current, reaches apeak current, and decays to a lower diffusion-limited current (DLC)level during the excitation. The initial current is substantiallydependent on the applied potential, while the DLC is not. If the scan isslow enough, the DLC may be seen as a plateau region in a voltammogram.

The DLC region represents a state where the oxidation or reduction ofthe measurable species at the conductor surface reaches a maximum ratesubstantially limited by diffusion. The diffusion may be limited by therate at which the measurable species travels from the sample to theconductor surface. Alternatively, when the working electrode of thesensor strip includes a DBL, the diffusion may be limited by the rate atwhich the measurable species travels from the DBL to the conductorsurface.

DLC values recorded at a relatively constant diffusion rate afterrehydration of the reagent layer may minimize inaccuracies that wouldotherwise be introduced by variations in the rehydration and diffusionrates of the reagents. Thus, once a relatively constant diffusion rateis reached, the recorded DLC values may more accurately correspond tothe concentration of the measurable species, and thus the analyte.

After completion of the forward excitation 610, for a cyclic or acyclicexcitation, such as those depicted in FIGS. 6B and 6C, respectively, areversed potential linear excitation 620 is applied. The reversedpotential linear scan of the excitation 620 may be applied atsubstantially the same rate as the forward scan 610. Thus, theexcitation range is scanned from a first lower value to a higher valueand back to a second lower value, where the first and second lowervalues may or may not be the same for cyclic or acyclic scans,respectively. Cyclic, and in some instances acyclic, excitations mayexamine the transition of a redox species from a reduced state to anoxidized state (and vice versa) in relation to the applied potential orin relation to the diffusion rate of the redox species to the conductorsurface.

In relation to a linear excitation, cyclic and acyclic excitations mayprovide a better representation of the DLC region of the excitation. Theadvantage of cyclic and acyclic excitations may be especiallyadvantageous for quantifying the DLC from quasi-reversible redox pairsat fast scan rates. Additional information about linear and cyclic scanvoltammetry may be found in “Electrochemical Methods: Fundamentals andApplications” by A. J. Bard and L. R. Faulkner, 1980.

FIG. 7A presents the data from a 25 mV/sec cyclic excitation of aferricyanide/ferrocyanide redox pair as a cyclic voltammogram. Thevoltammogram is characterized by a forward current peak during theforward portion of the scan from −0.3 V to +0.6 V indicatingferrocyanide oxidation and a reverse current peak during the reversevoltage scan from +0.6 V back to −0.3 V indicating ferricyanidereduction. The forward and reverse current peaks center around theformal potential E⁰′ of the ferrocyanide/ferricyanide redox pair, whenreferenced to the counter electrode. In this aspect, the potential ofthe counter electrode is substantially determined by the reductionpotential of ferricyanide, the major redox species present on thecounter electrode.

While the potentials where the forward and reverse scans begin (theexcitation range) may be selected to include the reduced and oxidizedstates of the redox pair, the excitation range may be reduced to shortenthe analysis time. However, the excitation range preferably includes theDLC region for the redox pair. For example, at a scan rate of 25 mV/sec,the concentration of the reduced [Red] and oxidized [Ox] species of theferrocyanide/ferricyanide reversible redox pair and the resultingelectrode potential are described by the Nernst equation as follows.

$\begin{matrix}{E = {E^{0^{\prime}} + {\frac{RT}{nF}\ln\;\frac{\lbrack{Ox}\rbrack}{\lbrack{Red}\rbrack}\underset{\underset{\_}{\_}}{T = {25{{{^\circ}C}.}}}E^{0^{\prime}}} + {\frac{0.059}{n}\log\frac{\lbrack{Ox}\rbrack}{\lbrack{Red}\rbrack}\underset{\underset{\_}{\_}}{n = 1}E^{0^{\prime}}} + {0.059\log\;\frac{\lbrack{Ox}\rbrack}{\lbrack{Red}\rbrack}}}} & (1)\end{matrix}$

In the Nernst equation, R is the gas constant of 8.314 Joul/(mole*K), Fis the Faraday constant of 96,5000 Coul./equiv., n is the number ofequivalents per mole, and T is the temperature in degrees Kelvin. Whenthe potential at the working electrode is referenced to its own redoxpotential, the formal potential E⁰′ will become substantially zero andthe equation collapses to:

$\begin{matrix}{E = {{0.059\log\;\frac{\lbrack{Ox}\rbrack}{\lbrack{Red}\rbrack}} = {0.059\;\log{\frac{\lbrack {{Fe}({CN})}_{6}^{- 3} \rbrack}{\lbrack {{Fe}({CN})}_{6}^{- 4} \rbrack}.}}}} & (2)\end{matrix}$From equation (2), when the ratio of the oxidized mediator to thereduced mediator changes by 10, the potential at the working electrodechanges by about 60 mV. The reverse is also true. Thus, for ferricyanide[Ox] to ferrocyanide [Red] concentration ratios of 10:1, 100:1, 1000:1and 10,000:1, the potential at the working electrode will beapproximately 60, 120, 180, and 240 mV away from the zero potential,respectively.

Thus, when the ratio of ferricyanide to ferrocyanide is ˜1000:1, a scanrange of −180 mV to +180 mV would provide substantially completeoxidation of the reduced species at the working electrode. At 180 mV,the oxidation rate is limited by how fast the reduced form of themediator can diffuse to the conductor surface, and from this potentialforward, there exists a DLC region. Thus, if the reversing point is set˜400 mV from the zero potential, ˜200 mV of DLC region may be provided.

For reversible systems, it may be preferable to provide an excitationrange of from 400 to 600 mV, thus exciting from 200 to 300 mV on eachside of the formal potential E⁰′ of the redox pair. For quasi-reversiblesystems, it may be preferable to provide an excitation range of from 600to 1000 mV, thus exciting from 300 to 500 mV on each side of the formalpotential E⁰′ of the redox pair.

The larger excitation range may be preferred for quasi-reversiblesystems because the DLC region may be smaller. In addition to redoxpairs that are inherently quasi-reversible, fast scan excitation maycause a redox pair that is reversible at slow excitation rates todemonstrate quasi-reversible behavior. Thus, it may be preferable toprovide a larger quasi-reversible excitation range for a reversibleredox pair at fast excitation rates.

Preferably, at least 25, 50, 100, 150, or 300 mV of DLC region isprovided by the selected excitation range. In another aspect, thereversing point for a cyclic or acyclic excitation is selected so thatfrom 25 to 400 mV, from 50 to 350 mV, from 100 to 300 mV, or from 175 to225 mV of DLC region is provided. For reversible systems, the reversingpoint for a cyclic or acyclic excitation may be selected so that from180 to 260 mV or from 200 to 240 mV of DLC region is provided. Forquasi-reversible systems, the reversing point for a cyclic or acyclicexcitation may be selected so that from 180 to 400 mV or from 200 to 260mV of DLC region is provided.

Once the reversing point is selected to provide the desired DLC region,the duration of the reverse scan may be selected for an acyclic scan. Ascan be seen in FIG. 7B, starting the forward scan and terminating thereverse scan at approximately −0.025 mV resulted in an acyclic scan thatincluded more of the forward current peak than the reverse current peak.From the FIG. 7B comparison, while the peak currents obtained for thecyclic (a) and acyclic (b) scans differ, the DLC region of the scanswere nearly the same, especially with regard to the reverse scan.

In another aspect, the reverse excitation may be terminated before thereverse current peak is reached, as depicted in FIG. 7C. When theforward excitation was started at a potential sufficiently negative,such as at −0.3 mV in FIG. 7C, to the middle of the potential range ofthe redox pair, such as −0.05 mV in FIG. 7C, the forward excitationincluded the full range of the redox potential of the redox pair. Thus,by terminating the reverse excitation at a potential from 50 to 500 mV,from 150 to 450, or from 300 to 400 mV negative from the reversingpoint, for example, the reverse current peak may be excluded for theferricyanide/ferrocyanide redox pair.

Similarly, the reverse excitation also may be terminated before thereverse current peak is reached by terminating the excitation when thereverse excitation current deviates in value from the DLC. A change inthe reverse excitation current of at least 2%, 5%, 10%, or 25% may beused to indicate the beginning of the reverse excitation current peak.

FIG. 7D compares a 1 V/sec cyclic voltammogram including the forward andreverse oxidation peaks of the redox pair with a 1 V/sec acyclicvoltammogram that excludes the forward and reverse oxidation peaks of aredox pair. The acyclic excitation had starting and ending points of 200mV and a reversing point of 300 mV. Preferable excitation ranges foracyclic excitations within the DLC region of theferricyanide/ferrocyanide redox pair, which exclude the forward andreverse oxidation and reduction peaks, are from 10 to 200 mV, morepreferably from 50 to 100 mV. While the cyclic voltammogram includingthe complete scan range significantly decayed after reaching the currentpeak, the acyclic voltammogram provided a substantially flat currentregion over the scan range. This current region may be directlycorrelated with the analyte concentration of the sample.

As seen in FIG. 7D, the current values recorded for the acyclicexcitation are numerically smaller than those of the cyclic excitation,while the background current is lower for the acyclic excitation. Thisbeneficial reduction in background current was unexpectedly obtainedwithout having to initiate the acyclic excitation in the reduction peakportion of the cyclic excitation. Thus, a fast and short acyclicexcitation within the DLC region of a redox pair may increase theaccuracy of analyte determination due to a reduction in the backgroundcurrent, which may provide an increase in the signal-to-backgroundratio.

Cyclic and acyclic excitations may provide multiple benefits in relationto linear excitations. In one aspect, the portion of the reverse scanfrom the reversing point to the point where the reverse current peakbegins may be a better representation of the true DLC values than theDLC region of the forward scan. The DLC region of the reverse excitationmay be a more accurate representation of analyte concentration forquasi-reversible redox systems or at fast excitation rates because theforward excitation may not show a distinct DLC region.

Acyclic excitations may have multiple advantages over cyclic excitationsincluding a shorter excitation time and a substantial decrease in theamount of mediator electrochemically converted to the measurable state.Thus, if the mediator is reduced in response to the analyte andelectrochemically oxidized during measurement, terminating the reverseexcitation before the oxidized mediator is electrochemically reduceddecreases the amount of reduced mediator in the sample not responsive tothe analyte. Similarly, starting the forward excitation at a potentialabove that at which the measurable species is reduced also may decreasethe amount of reduced mediator in the sample not responsive to theanalyte. Both acyclic excitations may allow for a shorter analysis time,a significant benefit for the user.

FIGS. 8A-8D show the output dynamic currents plotted as a function ofpotential from the pulse sequence of FIG. 6C using 7 triangular waveformexcitations for WB samples containing 40% hematocrit and 0, 50, 100, and400 mg/dL of glucose. The scan rate was 1 V/sec. Instead of aconventional long duration read pulse resulting in extensive oxidationof the measurable species, each triangular excitation was followed by arelaxation to provide a break in the current profile. The currents fromeach successive excitation were plotted as a different “rep” line, thusproviding rep1 through rep7 for each Figure.

The current values from each of the multiple excitations (each rep) inthe voltammograms of FIGS. 8A-8D were converted to a single data pointand connected to give the contour profiles of FIGS. 9A-9C. For FIGS. 9Aand 9B, the conversion was accomplished by selecting a current value atthe same potential in the DLC region of each successive excitation, suchas 300 mV. In FIG. 9A, the current values from FIGS. 8A-8D were directlyplotted as a function of time from the ending of the pulse sequence. InFIG. 9B, a semi-integral data treatment was applied to the currentvalues before plotting. For FIG. 9C, the multiple excitations wereconverted to single data points by selecting the peak current value ofeach rep and using a semi-derivative data treatment. In this manner, theX-axis of the contour profiles are expressed in terms of time, thusmimicking the data obtained from a conventional system at steady-state,where the current change with time is substantially constant. While therecorded voltammogram currents may be treated in multiple ways toextract useful information, semi-integral, semi-derivative, andderivative data treatments are presently preferred.

The dynamic current profiles obtained from gated voltammetric pulsesequences are fundamentally different from the current profiles obtainedfrom a conventional analysis using a single read pulse. While currentsrecorded from a single read pulse derive from a singlerelaxation/diffusion, each time point in the contour profile of thedynamic currents originates from an excitation after an independentrelaxation/diffusion process. Furthermore, as the length of anexcitation increases, the correlation between the current and theanalyte concentration may decrease, often due to the hematocrit effect.Thus, the accuracy of an analysis using multiple, short excitations maybe increased in comparison to an analysis using a longer read pulsehaving the duration of the multiple excitations combined.

The application of these data treatments to glucose analysis isdescribed below. However, a more in-depth discussion of data treatmentsfor transforming electrochemical currents and the related digitalimplementations may be found in Bard, A. J., Faulkner, L. R.,“Electrochemical Methods: Fundamentals and Applications,” 1980; Oldham,K. B.; “A Signal-independent Electroanalytical Method,” Anal. Chem.1972, 44, 196; Goto, M., Oldham, K. B., “Semi-integral Electroanalysis:Shapes of Neopolarograms,” Anal. Chem. 1973, 45, 2043; Dalrymple-Alford,P., Goto, M., Oldham, K. B., “Peak Shapes in Semi-differentialElectroanalysis,” Anal. Chem. 1977, 49, 1390; Oldham, K. B.,“Convolution: A General Electrochemical Procedure Implemented by aUniversal Algorithm,” Anal. Chem. 1986, 58, 2296; Pedrosa, J. M.,Martin, M. T., Ruiz, J. J., Camacho, L., “Application of the CyclicSemi-integral Voltammetry and Cyclic Semi-Differential Voltammetry tothe Determination of the Reduction Mechanism of a Ni-Porphyrin,” J.Electroanal. Chem. 2002, 523, 160; Klicka, R, “Adsorption inSemi-Differential Voltammetry,” J. Electroanal. Chem. 1998, 455, 253.

Semi-integration of a voltammogram may separate the DLC from thehematocrit affected equilibrium current (initial peak) because separatesignals may be observed for the hematocrit-affected equilibrium sicurrent and the hematocrit. This is especially true at slow scan rates.The semi-integral of the experimentally obtained voltammetric currenti(t) has the following mathematical form:

$\begin{matrix}{{\frac{\mathbb{d}^{{- 1}/2}}{\mathbb{d}t^{{- 1}/2}}{i(t)}} = {{I(t)} = {\frac{1}{\pi^{1/2}}{\int_{0}^{t}{\frac{i(u)}{( {t - u} )^{1/2}}{\mathbb{d}u}}}}}} & (3)\end{matrix}$

where

i(t) is the time function of the voltammetric current obtained duringthe scan;

I(t) is a transformation and the semi-integral of i(t);

u is a transformation parameter; and

-   d^(−1/2)/dt^(−1/2) is the semi-integration operator.

At a sufficiently high oxidation potential, the steady-statesemi-integral current is given by:I _(lim) =nFAD^(1/2) C (coul/sec^(1/2))  (4)

where I_(lim) is the DLC under the condition of the surfaceconcentration of the oxidizable species being zero. Note that the unitof semi-integral current is coul/sec^(1/2), which is not the traditionalunit for expressing electrical current, which is coul/sec.

For simplicity, I_(lim) is referred to as the semi-integration DLC(SI)with a unit of coul/sec^(1/2). This SI current (coul/sec^(1/2)) is onlya half-step integration from current (coul/sec). The half-stepintegration is fundamentally different from coulometry where a fullintegral is applied to the i-t curve to provide the total charge passingthrough the electrodes.

Although equation (3) gives a theoretical definition of thesemi-integral, for digital processing the i−t data may be divided into Nequally spaced time intervals between t=0 and t=NΔt. One such digitalprocessing algorithm is given by equation (5) where t=kΔt and u=jΔt, andi is determined at the midpoint of each interval.

$\begin{matrix}{{I( {k\;\Delta\; t} )} = {\frac{1}{\pi^{1/2}}{\sum\limits_{j = 1}^{j = k}\frac{{i( {{j\;\Delta\; t} - {{1/2}\Delta\; t}} )}\;\Delta\; t^{1/2}}{\sqrt{k - j + {1/2}}}}}} & (5)\end{matrix}$

A preferred algorithm for digital processing is given by:

$\begin{matrix}{{I( {k\;\Delta\; t} )} = {\frac{1}{\pi^{1/2}}{\sum\limits_{j = 1}^{j = k}{\frac{\Gamma( {k - j + {1/2}} )}{( {k - j} )!}\Delta\; t^{1/2}{i( {j\;\Delta\; t} )}}}}} & (6)\end{matrix}$where Γ(x) is the gamma function of x, where Γ(½)=π^(1/2), Γ(3/2)=½π^(1/2), and Γ( 5/2)= 3/2*½π^(1/2), etc.

From equation (4) it may be seen that the SI current lacks thetime-dependence factor of conventional amperometric methods. Thus, theSI current response may be considered a series of plateau currents,instead of the continuously changing amperometric currents obtained fromconventional amperometry. Because the semi-integration allows forquantification of the DLC, a faster scan rate may be used than when peakcurrents are quantified. Thus, linear, cyclic, or acyclic voltammetry incombination with semi-integration may rapidly generate a DLC in responseto glucose concentrations. In this manner, the disadvantages of the longwait times of coulometry and the non-steady-state nature of the currentin conventional amperometry may be reduced.

Equation (4) also shows that reversible or quasi-reversible redox pairsare preferred for use with semi-integration. This is because thesemi-integral from a reversible or quasi-reversible redox pair canexhibit a sharp transition from the reduced state to the oxidized state(and vice versa) and a wide DLC region, thus making the transitioneasier to determine. Ferricyanide/ferrocyanide and the +3 and +2 statesof ruthenium hexaamine are examples of redox pairs demonstratingpreferred reversible (slow scan) or quasi-reversible (fast scan)behaviors.

Poorly activated electrodes may not provide an acceptable DLC conditioneven with reversible or quasi-reversible redox pairs. Thus, electrodeactivation procedures, such as those described in U.S. Pat. No.5,429,735, may be used to achieve the preferred electrode activity.

In addition to semi-integrals, semi-derivatives of a voltammogram alsomay be used to quantify the analyte by measuring the peak of thesemi-derivative. The semi-derivative of the experimentally obtainedvoltammetric current i(t) has the following mathematical forms:

$\begin{matrix}{\frac{\mathbb{d}^{1/2}}{\mathbb{d}t^{1/2}}{i(t)}} & (7)\end{matrix}$

$\begin{matrix}{{{\frac{\mathbb{d}^{1/2}}{\mathbb{d}t^{1/2}}{i(t)}} = {\frac{\mathbb{d}{I(t)}}{\mathbb{d}t} = {\frac{\mathbb{d}}{\mathbb{d}t}\lbrack {\frac{1}{\pi^{1/2}}{\int_{0}^{t}{\frac{i(u)}{( {t - u} )^{1/2}}{\mathbb{d}u}}}} \rbrack}}},( {\text{coul}\text{/}\sec^{3/2}} )} & (8)\end{matrix}$where I(t) is the semi-integral of the time function i(t). The equationsused for the semi-integral, semi-derivative, and the derivative datatreatment described below, were implemented with the ElectrochemicalWorkstation software package, version 4.07, revised Apr. 26, 2004, whichaccompanies the CH Instruments Electrochemical Workstation, model CHI660A.

FIG. 10A presents the semi-integral plot of the cyclic voltammogram fromFIG. 7A. Similarly, FIG. 10B presents the semi-integral plot of theacyclic voltammogram from FIG. 7C, where the reverse excitationterminated before initiation of the reverse current peak. FIG. 10Cestablishes that when the semi-integral of the cyclic and acyclicexcitations of FIG. 7B are plotted, the DLC region of the return scanwas readily established, permitting an accurate current reading in aslittle as 50 mV from the reversing point. Furthermore, the peak portionof the semi-integral plot was responsive to the hematocrit content ofthe sample and the magnitude of the peak may be quantitatively relatedto the hematocrit level.

FIG. 10D shows the semi-integrals for the cyclic and 200 to 300 mVacyclic excitations of FIG. 7D. The shape of the si voltammogram fromthe short acyclic excitation differs from the voltammogram of the cyclicexcitation because the region of oxidation-reduction transition ismissing from the acyclic excitation. By starting the acyclic excitationin the DLC region, the background si current decreased at a faster ratein comparison to that observed for the cyclic voltammogram, thusimproving the signal-to-background ratio for the acyclic excitation.Furthermore, the reverse si current from the acyclic excitation shows aplateau more accurately describing the analyte concentration of thesample than the forward si current. In this manner, the acyclic scan ofthe DLC region provided an increase in accuracy for the analysis whencompared to the cyclic excitation.

FIG. 11 shows contour profiles prepared by semi-integratingvoltammograms from a seven excitation pulse sequence for WB samplescontaining 0, 56, 111, 221.75, 455.25, and 712.5 mg/dL of plasmaglucose. For each of the glucose concentrations, equilibrium withregards to DBL rehydration was reached at the highest current value inthe contour profile for each glucose concentration. Thus, readings 1110(highest) and 1120 (lower) establish that equilibrium was reachedregarding DBL rehydration at about four seconds for the 455 mg/dLglucose concentration.

Current values recorded at a relatively constant diffusion rate mayminimize inaccuracies that would otherwise be introduced by variationsin the rehydration and diffusion rates of the reagents. Thus, once arelatively constant diffusion rate is reached, the recorded currentvalues may more accurately correspond to the concentration of themeasurable species, and thus the analyte. Furthermore, for FIG. 11, thecomplete analysis may be completed in as few as seven seconds becauseonce the highest current value 1110 of the contour profile is known, itsvalue may be directly correlated to the analyte concentration.Additional data points may be obtained to reduce background errorattributable to the mediator, as previously discussed with regard to RI.

Another form of data treatment that may be used to generate a contourprofile is semi-derivatization. One implementation of a semi-derivativeis to take a full step derivative of the semi-integral, as previouslydescribed in relation to equation (8). Unlike the plateau regionrepresenting the voltammetric scan in semi-integral plots,semi-derivative plots convert the voltammetric scan data into a peakcentered at the transition of the redox pair.

FIG. 12A depicts the cyclic voltammogram (a), semi-integral (b), andsemi-derivative (c) of 16 mM ferrocyanide in a 20% hematocrit WB sample.In this instance, the working electrode of the sensor strip lackedenzyme and oxidized mediator. FIG. 12B is an enlargement of thesemi-derivative curve of FIG. 12A showing the peak height for theforward scan. The value of the forward or reverse scan peak height maybe correlated with the analyte concentration of the sample. Furthermore,the semi-derivative data treatment may inherently provide hematocritcompensation for glucose determination, especially for samples includingless than 40% hematocrit. A more detailed description of the applicationof semi-derivative data treatment to glucose analysis may be found in WO2005/114164, filed May 16, 2005, entitled “Voltammetric Systems forAssaying Biological Analytes.”

In addition to semi-integral and semi-derivative data treatments, aderivative data treatment also may be used to generate a contourprofile, and thus determine the concentration of the analyte in thesample. FIGS. 13A-13C depict the derivatives of cyclic voltammograms forsamples having 20, 40, and 60% hematocrit. These derivative plots showan initial increase in current as voltage increases, followed by adecrease, and finally a DLC region. The hematocrit effect may be seen inthe negative peak located at about 0.1 volts in FIGS. 12A-12C, withhigher RB cell concentrations reflected as more negative peak values.

While the values of the positive and negative derivative peaks, such asthose depicted in the derivative plot of FIG. 13B, are concentrationdependent, the ratio of the negative peak to the positive peak cancelsout the concentration dependence, thus being hematocrit dependent.Because this ratio (HI-DER) is concentration independent and hematocritdependent, the ratio indicates the percent hematocrit in the sample.Thus, this ratio of the derivative peaks may be used to determine ahematocrit compensation equation for analyte determination. A moredetailed description of the application of derivative data treatment toglucose analysis may be found in WO 2005/114164.

In addition to the ability of the gated pulse sequences to reduceinaccuracy from the hematocrit effect and from the mediator backgroundsignal, the combination of the dynamic current profile of eachexcitation and the resulting contour profiles may be used to providemultiple sets of calibration constants to the sensor system, thusincreasing the accuracy of the analysis. Each set of calibrationconstants obtained may be used to correlate a specific current readingto a specific concentration of measurable species in the sample. Thus,in one aspect, an increase in accuracy may be obtained by averaging theglucose values obtained using multiple sets of calibration constants.

Conventional electrochemical sensor systems generally use one set ofcalibration constants, such as slope and intercept, to convert currentreadings into a corresponding concentration of the analyte in thesample. However, a single set of calibration constants may result ininaccuracies in the analyte concentration determined from the recordedcurrent values because random noise is included in the measurement.

By taking the current value or the transformed current value after datatreatment at a fixed time within each duty cycle of a gated voltammetricpulse sequence, multiple sets of calibration constants may beestablished. FIG. 14 plots the semi-integral currents recorded at 7.4,10.65, 13.9, and 17.15 seconds for the contour profiles of FIG. 11. Eachof these four calibration lines are independent of the other and may beused in at least two ways.

First, the multiple sets of calibration constants may be used todetermine the number of duty cycles that should be applied during thepulse sequence to obtain the desired accuracy and precision. Forexample, if the current values obtained from the first three excitationsindicate a high glucose concentration, such as >150 or 200 mg/dL, thesensor system may terminate the analysis early, such as after the 4^(th)excitation depicted in FIG. 11. In this manner, the time required forthe analysis may be substantially shortened. Such a shortening may bepossible because imprecision at high glucose concentrations is typicallyless than at lower glucose concentrations. Conversely, if the currentvalues obtained from the first three excitations indicate a low glucoseconcentration, such as ≦150 or 100 mg/dL, the sensor system may extendthe analysis to greater than 5 or 7 excitations. Thus, the accuracyand/or precision of the analysis may be increased by including 5 or moreduty cycles.

Second, the multiple sets of calibration constants may be used toincrease the accuracy and/or precision of the analysis by averaging. Forexample, if the target glucose measurement time is 17.15 seconds, thecurrents at 10.65, 13.9, and 17.15 seconds can be utilized to calculatethe glucose concentrations using the slopes and intercepts from thecorresponding calibration lines; therefore,G_(10.65)=(i_(10.65)−Int_(10.65))/Slope_(10.65),G_(13.9)=(i_(13.9)−Int_(13.9))/Slope_(13.9), andG_(17.15)=(i_(17.15)−Int_(17.15))/Slope_(17.15). Theoretically, thesethree glucose values should be equivalent, differing only by randomvariations. Thus, the glucose values G_(10.65), G_(13.9), and G_(17.15)may be averaged and the final glucose value of(G_(10.65)+G_(13.9)+G_(17.15))/3 may be calculated. Averaging the valuesfrom the calibration lines may provide a reduction in noise at the rateof 1/√3).

An unexpected benefit of gated voltammetric pulse sequences includingrelatively short excitations and relatively long relaxations, such asthat depicted in FIG. 6C, is the ability to simplify calibration. Whilethe multiple sets of calibration constants that may be obtained from thedynamic and contour profiles may provide an advantage to the accuracy ofthe analysis, a pulse sequence such as depicted in FIG. 6C, may providesimilar accuracy to that obtained using multiple sets of calibrationconstants from a single set of calibration constants. This effect may beobserved in the contour profiles of FIG. 11 and the resultingcalibration lines in FIG. 14.

This unexpected increase in accuracy may be attributable to therelatively long relaxation times in comparison to the short relaxations.In one aspect, excitation/relaxation time (ERT) ratios from 0.3 to 0.2are preferred, with ERT ratios from 0.27 to 0.22 being more preferred.For example, a gated voltammetric pulse sequence having an ERT ratio of0.25 (0.8 seconds/3.2 seconds), such as depicted in FIG. 6C, may bepreferred to a pulse having an ERT ratio of greater than 0.3, such asthe FIG. 6B pulse sequence having an ERT ratio of 0.56 (1.4 seconds/2.5seconds). While not intending to be bound by any particular theory, therelatively long relaxation times may provide a state where the averageconsumption rate of measurable species during the excitation is balancedby the supply rate of measurable species diffusing into the DBL. In thismanner, the multiple sets of calibration constants may collapse into asingle set and the conversion of the recorded data into an analyteconcentration may be simplified by carrying out the averaging process onthe recorded current data before determining the analyte concentration.

The dynamic current profiles provided by the multiple duty cycles may beused to determine if the sensor strip has been under-filled with sample,thus allowing the user to add additional sample to the sensor strip. Inaddition to working and counter electrodes, conventional sensor systemsmay determine an under-fill condition through the use of a thirdelectrode or electrode pair; however, the third electrode or electrodepair adds complexity and cost to the sensor system.

Conventional two electrode systems may be able to recognize that ananalysis is “bad,” but may not determine if the reason for the failedanalysis was caused by under-fill or a defective sensor strip. Theability to determine if under-fill caused the failure of the analysis isbeneficial because it may be corrected by adding additional sample tothe same sensor strip and repeating the analysis, thus preventing a goodstrip from being discarded.

FIG. 15 depicts the cyclic voltammograms obtained from an under-filledsensor strip, while FIG. 8A depicts a series of seven cyclicvoltammograms obtained with a gated voltammetric pulse sequence from anormal-filled sensor strip. In both instances, the scan rate was 1V/sec. Even though the FIG. 8A sample lacked any glucose and the sampleused for FIG. 15 included 400 mg/dL of glucose, the current valuesobtained from the under-filled strip having the 400 mg/dL glucoseconcentration were much lower than those from the normal-filled striphaving no glucose. Thus, it may be determined by the second duty cycleof the pulse sequence that the currents obtained are lower than apreviously selected value and that the sensor strip is under-filled. Forexample, for the system of FIG. 15, initial current values less than 0signify that the sensor strip is under-filled.

In this manner, the gated voltammetric pulse sequences of the presentinvention allowed for under-fill detection in a two-electrode sensorstrip, a function typically requiring a third electrode for conventionalsensor systems. Furthermore, the under-fill determination may be made inless than 5 seconds, providing time for the measuring device to signalthe user, such as by sending a signal to a light emitting device or adisplay, to add more sample to the strip.

A common problem for the accuracy of strip based analysis methods isthat the reagents, especially the enzyme, degrade over time. One of theeffects of enzyme degradation is a change in the calibration values, andthus the precision and/or accuracy of the analysis.

The dynamic current profiles provided by the multiple duty cycles of thepresent invention may be used to determine the active ionizing agentcontent of aged sensor strips, where the ionizing species may havedegraded. Knowing the amount of ionizing agent available to react withthe analyte may allow for the identification of defective sensor stripsand for the correction of the analyte concentration value to provide thedesired accuracy and precision to the analysis. In this manner, theaccuracy and/or precision of the analysis obtained from sensor stripshaving varying amounts of active ionizing agent due to manufacturingvariability or reagent degradation may be obtained.

FIG. 16A depicts semi-integral plots of cyclic voltammograms obtainedfrom five sensor strips with 1 V/sec scan rates for a sample including100 mg/dL glucose and 40% hematocrit in WB. While FIG. 16A presentsacyclic voltammograms, the method also may be applied to cyclic scans.The ionizing agent used in the reagent layer for the sensor strips wasthe glucose oxidase (GO) enzyme. Each sensor strip included a dry weightpercentage of 1.7, 3.5, 5.3, 7, or 10 percent (weight/weight) GO inrelation to the total dry weight of the material forming the regentlayer. As seen in the figure, the current values for the forward scansincrease in relation to those for the reverse scans as the percentage ofionizing agent increases. Thus, the difference between the forward andreverse scan current values may be used to determine the percent ofactive ionizing agent present in the reagent layer of the sensor strip.

FIG. 16B plots the ratio of the forward and reverse scan si currentvalues taken at the 0.15 potential as a function of percent GO. Once thecorrelation between the forward and reverse current ratios and thepercent active GO is determined, the amount of active GO present in areagent layer may be determined from the current values measured for astrip. The ratio of the forward and reverse scans may be determinedbefore or during the analyte analysis portion of the pulse sequence,thus allowing the user to be notified if the strip is defective.

The actual active ionizing agent content of the strip may then be usedto alter the calibration slope through a relationship such as shown inFIG. 16C. FIG. 16C depicts a typical response of the slope of the linearresponse calibration of the sensor strip as a function of the GO content(%-dry weight). This plot shows that as the GO content increases, thecalibration slope decreases. Thus, if the actual GO content of thereagent layer is calculated from FIG. 16B, the affected slope of theGO-based sensor strip may be calculated from the 2^(nd) order polynomialof FIG. 16C using the GO content as the input. The output slope then maybe used to correct the glucose concentration value in response todiffering amounts of active ionizing agent present in the reagent layerof the sensor strip. In this manner, inaccuracy and/or imprecision thatwould otherwise result from enzyme degradation may be reduced.

FIG. 17 is a schematic representation of a measuring device 1700including contacts 1720 in electrical communication with electricalcircuitry 1710 and a display 1730. In one aspect, the measuring device1700 is portable and is adapted to be handheld and to receive a sensorstrip, such as the strip 100 from FIG. 1A. In another aspect, themeasuring device 1700 is a handheld measuring device adapted to receivea sensor strip and implement gated voltammetric pulse sequences.

The contacts 1720 are adapted to provide electrical communication withthe electrical circuitry 1710 and the contacts of a sensor strip, suchas the contacts 170 and 180 of the sensor strip 100 depicted in FIG. 1B.The electrical circuitry 1710 may include an electric charger 1750, aprocessor 1740, and a computer readable storage medium 1745. Theelectrical charger 1750 may be a potentiostat, signal generator, or thelike. Thus, the charger 1750 may apply a voltage to the contacts 1720while recording the resulting current to function as a charger-recorder.

The processor 1740 may be in electrical communication with the charger1750, the computer readable storage medium 1745, and the display 1730.If the charger is not adapted to record current, the processor 1740 maybe adapted to record the current at the contacts 1720.

The computer readable storage medium 1745 may be any storage medium,such as magnetic, optical, semiconductor memory, and the like. Thecomputer readable storage medium 1745 may be a fixed memory device or aremovable memory device, such as a removable memory card. The display1730 may be analog or digital, in one aspect a LCD display adapted todisplaying a numerical reading.

When the contacts of a sensor strip containing a sample are inelectrical communication with the contacts 1720, the processor 1740 maydirect the charger 1750 to apply a gated voltammetric pulse sequence tothe sample, thus starting the analysis. The processor 1740 may start theanalysis in response to the insertion of a sensor strip, the applicationof a sample to a previously inserted sensor strip, or in response to auser input, for example.

Instructions regarding implementation of the gated voltammetric pulsesequence may be provided by computer readable software code stored inthe computer readable storage medium 1745. The code may be object codeor any other code describing or controlling the functionality describedin this application. The data that results from the gated voltammetricpulse sequence may be subjected to one or more data treatments,including the determination of decay rates, K constants, slopes,intercepts, and/or sample temperature in the processor 1740 and theresults, such as a corrected analyte concentration, output to thedisplay 1730. As with the instructions regarding the pulse sequence, thedata treatment may be implemented by the processor 1740 from computerreadable software code stored in the computer readable storage medium1745.

EXAMPLES Example 1 Collection of Voltammetric Data

The cyclic voltammogram of FIG. 7A was obtained from a CHElectrochemical Work Station by applying a potential between the workingand counter electrodes of a sensor strip that varied linearly by 1 V/secat a scan rate of 0.025 V/sec. The current generated at the workingelectrode during the application of the potential was recorded andplotted as a function of the applied potential. After the initial 0.8second excitation, the potentiostat opened the circuit to provide a 3.2second relaxation. Six additional excitations were applied to the stripusing the pulse sequence of FIG. 6C. In this manner, seven acyclicvoltammograms for glucose concentrations of 0, 50, 100, and 400 mg/dL,as shown in FIGS. 8A-8D, respectively, were obtained.

Example 2 Establishing Contour Plots for Multiple Data Treatments

FIGS. 9A, 9B, and 9C are contour plots from unprocessed voltammetriccurrents, semi-integral, and semi-derivative data treatments,respectively. In FIG. 9A, unprocessed current values at 0.3 V were takenfrom each forward scan to provide seven data points. The resultingcontour plot presents the unprocessed current values as a function oftime since each duty cycle included a 0.8 second excitation followed bya 3.2 second relaxation.

FIG. 9B presents a contour plot of the same voltammetric data convertedwith semi-integral data processing according to equation (3) andimplemented with equations (5) and (6). The implemented semi-integraldata processing was that present in the CH Electrochemical Work Stationsoftware package, version 4.07, revised Apr. 26, 2004, which accompaniesthe CH Instruments Electrochemical Workstation, model CHI 660A. Aftersemi-integral processing, the semi-integral currents at 0.3 V were takenfrom the reverse portion of each scan and plotted as function of time,as previously described with regard to FIG. 9A.

FIG. 9C presents a contour plot of the same voltammetric data convertedwith semi-derivative data processing according to equation (8). Thesemi-derivative data processing used was that present in the CHElectrochemical Work Station software package, version 4.07, revisedApr. 26, 2004, which accompanies the CH Instruments ElectrochemicalWorkstation, model CHI 660A. After semi-derivative processing, the peakcurrent value was taken from each scan and plotted as function of time,as previously described with regard to FIGS. 9A and 9B. Thus, the Y-axisof FIG. 9C has the unit of uCoul/sec^(3/2) for the semi-derivativecurrents.

Example 3 Constructing Calibration Plots and Determining AnalyteConcentration

As shown in FIG. 14, a calibration plot for the semi-integral dataprocessing method was formed by taking the semi-integral currents fromthe four different glucose concentration at 8.8, 12.8, 16.8, and 20.8seconds from FIG. 9B and plotting the currents as a function of YSIplasma glucose concentration. Glucose sample concentrations weredetermined from the calibration plot by plugging in the semi-integralprocessed current from a sample measurement at a specific time into theslope and intercept of the calibration line.

Calibration plots for the unprocessed and semi-derivative processed datawere generated similarly. The calibration plots were then used todetermine glucose sample concentrations from unprocessed andsemi-derivative processed measured current values taken at a specifictime.

Example 4 Determining Analyte Concentration from Multiple CalibrationSets

FIG. 4 depicts at least four calibration lines for times up to 20.8seconds. For an analysis time of 16.8 seconds, the calibration points at8.8 and 12.8 seconds were used to calibrate the glucose values. Thethree glucose values calculated from the 8.8, 12.8 and 16.8 secondcalibration points were the result of independent oxidations separatedby the relaxation time before the 8.8, 12.8 and 16.8 second excitation.While representing the same sample glucose concentration, theconcentration values differ by the experimental noise. Thus, byaveraging, G=(G_(8.8)+G_(12.8)+G_(16.8))/3, these values, thesignal-to-noise ratio of the final glucose concentration value wasincreased.

While various embodiments of the invention have been described, it willbe apparent to those of ordinary skill in the art that other embodimentsand implementations are possible within the scope of the invention.

The invention claimed is:
 1. In an electrochemical method fordetermining the concentration of an analyte in a sample, where themethod includes applying an input signal to a sensor strip so theanalyte undergoes a redox reaction to generate an electric current thatis measured and correlated with the concentration of the analyte in thesample, the sensor strip including electrodes and reagents, where thereagents include an oxidoreductase and react with and transfer electronsfrom the analyte to the electrodes; the improvement comprising applyinga gated voltammetric pulse sequence to the sample comprising at leasttwo duty cycles, where each of the duty cycles includes an excitationand a relaxation, the relaxation is from 0.1 to 3 seconds, and therelaxation includes a current reduction to one-half or less of thecurrent flow at the excitation maxima.
 2. The electrochemical method ofclaim 1, where the relaxation includes a current reduction to a zerocurrent flow state.
 3. The electrochemical method of claim 1, where therelaxation is provided by an open circuit.
 4. The electrochemical methodof claim 3, where during the relaxation the oxidoreductase reacts withthe analyte to generate measurable species without the effects of anelectric potential.
 5. A voltammetric method for determining theconcentration of an analyte in a sample, comprising: applying a pulsesequence to the sample, the pulse sequence having at least two dutycycles, where each of the duty cycles includes an excitation and arelaxation, where the excitation includes a potential varied with time,and where the relaxation is from 0.1 to 3 seconds and includes a currentreduction to at least one-half the current flow at the excitationmaxima; measuring resulting currents from at least one of theexcitations including the potential varied with time; and determiningthe concentration of the analyte in the sample from at least one of theresulting currents.
 6. The method of claim 5, where the relaxationincludes a current flow reduction to at least an order of magnitude lessthan the current flow at the excitation maxima.
 7. The method of claim5, where the relaxation includes a current reduction to a zero currentflow state.
 8. The method of claim 5, where the excitation is from 0.1to 1.5 seconds.
 9. The method of claim 5, where the relaxation is from0.1 to 2 seconds.
 10. The method of claim 5, where the pulse sequencecomprises at least three duty cycles within 90 seconds.
 11. The methodof claim 5, where the pulse sequence comprises at least three dutycycles within 5 seconds.
 12. The method of claim 5, where thedetermining the concentration of the analyte in the sample is completein from 2 to 50 seconds.
 13. The method of claim 5, where the pulsesequence comprises a terminal read pulse.
 14. The method of claim 5,further comprising applying the pulse sequence to a sensor stripincluding a counter electrode and a diffusion barrier layer on a workingelectrode.
 15. The method of claim 5, further comprising determining theconcentration of the analyte in the sample with less bias attributableto mediator background than a concentration of the analyte determined inresponse to resulting currents measured from a pulse sequence lackingthe at least two duty cycles.
 16. The method of claim 5, where thesample is a liquid comprising a biological fluid.
 17. The method ofclaim 5, where the analyte is glucose.
 18. The method of claim 5, wherethe excitation comprises a potential varied linearly at a rate of atleast 2 mV/sec.
 19. The method of claim 18, where the excitation isselected from the group consisting of linear, cyclic, acyclic, andcombinations thereof.
 20. The method of claim 18, where at least tworesulting current values are recorded during the excitation.
 21. Themethod of claim 5, where the excitations are acyclic and substantiallyexclude a reverse oxidation peak or a reverse reduction peak of ameasurable species responsive to the concentration of the analyte in thesample.
 22. The method of claim 21, further comprising determining theconcentration of the analyte in the sample with less bias from ameasurable species not responsive to the concentration of the analyte inthe sample than a concentration of the analyte in the sample determinedin response to a pulse sequence including cyclic excitations.
 23. Themethod of claim 5, where the excitations are acyclic and terminatebefore initiation of a reverse current peak.
 24. The method of claim 5,where the excitations are acyclic and substantially exclude forward andreverse oxidation and reduction peaks of a measurable species responsiveto the concentration of the analyte in the sample.
 25. The method ofclaim 5, where the excitations are acyclic and are substantially withina diffusion limited current region of a redox pair.
 26. The method ofclaim 5, further comprising determining at least one contour profilefrom the resulting currents.
 27. The method of claim 5, furthercomprising applying at least one data treatment selected from the groupconsisting of semi-integral, semi-derivative, and derivative to theresulting currents.
 28. The method of claim 5, further comprisingdetermining a plurality of calibration sets from the resulting currents.29. The method of claim 28, further comprising determining the number ofduty cycles of the pulse sequence from the plurality of calibrationsets.
 30. The method of claim 29, where the determining of theconcentration of the analyte in the sample comprises averaging multipleconcentration values obtained from the plurality of calibration sets.31. The method of claim 5, further comprising comparing at least oneresulting current to a pre-selected value; and determining if a sensorstrip containing the sample is under-filled with the sample from thecomparison.
 32. The method of claim 5, further comprising determining aratio from forward and reverse scan resulting currents; and determiningan active ionizing agent content of a sensor strip.
 33. The method ofclaim 32, where the ratio was previously correlated to known amounts ofthe active ionizing agent.
 34. The method of claim 32, furthercomprising altering a calibration slope in response to the activeionizing agent content of the sensor strip.
 35. The method of claim 5,where an excitation/relaxation time ratio of the duty cycles is from 0.3to 0.2.
 36. The method of claim 35, further comprising determining theconcentration of the analyte in the sample more accurately than aconcentration of the analyte in the sample determined in response toresulting currents from a pulse sequence having an excitation/relaxationtime ratio of the duty cycles greater than 0.3.
 37. The method of claim5, further comprising determining a plurality of calibration sets fromresulting currents recorded during the at least two duty cycles; anddetermining a duration of the pulse sequence in response to thedetermined concentration of the analyte in the sample.
 38. The method ofclaim 5, further comprising: comparing at least one resulting current toa pre-selected value; determining if a sensor strip is under-filled fromthe comparison; and signaling to add additional sample to the sensorstrip if the strip is under-filled.
 39. The method of claim 38, wheresignaling occurs in less than 5 seconds.
 40. The electrochemical methodof claim 5, where the relaxation is provided by an open circuit.
 41. Theelectrochemical method of claim 40, where during the relaxation anionizing agent reacts with the analyte to generate measurable specieswithout the effects of an electric potential.